Решения NCERT класса 8 — Глава 14 Факторизация — Упражнение 14.4
Найдите и исправьте ошибки в следующих математических утверждениях:
Вопрос 1. 4(х – 5) = 4х – 5
Решение:
Given: 4(x – 5) = 4x – 5
Now we check if the given statement is correct or not
Taking L.H.S:
= 4(x – 5)
= 4x – 20
L.H.S ≠ R.H.S
So, the correct solution of 4(x – 5) = 4x – 20
Вопрос 2. х(3х + 2) = 3х 2 + 2
Решение:
Given: x(3x + 2) = 3x2+ 2
Now we check if the given statement is correct or not
Taking L.H.S:
= x(3x + 2)
= 3x2 + 2x
L.H.S ≠ R.H.S
So, the correct solution of x(3x + 2) = 3x2+ 2x
Вопрос 3. 2x + 3y = 5xy
Решение:
Given: 2x + 3y = 5xy
Here, L.H.S ≠ R.H.S
So, the correct solution of 2x + 3y = 2x + 3y
Вопрос 4. х + 2х + 3х = 5х
Решение:
Given: x + 2x + 3x = 5x
Now we check if the given statement is correct or not
Taking L.H.S:
= x + 2x + 3x
= 6x
L.H.S ≠ R.H.S
So, the correct solution of x + 2x + 3x = 6x
Вопрос 5. 5у + 2у + у – 7у = 0
Решение:
Given: 5y + 2y + y – 7y = 0
Now we check if the given statement is correct or not
Taking L.H.S:
= 5y + 2y + y – 7y
= y
L.H.S ≠ R.H.S
So, the correct solution of 5y + 2y + y – 7y = y
Вопрос 6. 3x + 2x = 5x 2
Решение:
Given: 3x + 2x = 5x2
Now we check if the given statement is correct or not
Taking L.H.S:
= 3x + 2x
= 5x
L.H.S ≠ R.H.S
So, the correct solution of 3x + 2x = 5x
Вопрос 7. (2x) 2 + 4(2x) + 7 = 2x 2 + 8x + 7
Решение:
Given: (2x)2+ 4(2x) + 7 = 2x2+ 8x + 7
Now we check if the given statement is correct or not
Taking L.H.S:
= (2x)2+ 4(2x) + 7
= 4x2 + 8x + 7
L.H.S ≠ R.H.S
So, the correct solution of (2x)2+ 4(2x) + 7 = 4x2 + 8x + 7
Вопрос 8. (2x) 2 + 5x = 4x + 5x = 9x
Решение:
Given: (2x)2+ 5x = 4x + 5x = 9x
Here,
4x + 5x ≠ 9x
So, we check (2x)2+ 5x = 4x + 5x or not
Taking L.H.S:
= (2x)2+ 5x
= 4x2 + 5x
L.H.S ≠ R.H.S
So, the correct solution of (2x)2+ 5x = 4x2 + 5x
Вопрос 9. (3х+2) 2 = 3х2 +6х+4
Решение:
Given: (3x + 2)2= 3x2+ 6x + 4
Now we check if the given statement is correct or not
Taking L.H.S:
= (3x + 2)2
= 9x2 + 6x + 4
L.H.S ≠ R.H.S
So, the correct solution of (3x + 2)2 = 9x2 + 6x + 4
Вопрос 10. Подставив x = – 3 в
(a) x 2 + 5x + 4 дает (– 3) 2 + 5 (-3) + 4 = 9 + 2 + 4 = 15
Решение:
Given: x2+ 5x + 4
Now substitute the value of x = -3 in the given equation,
= (-3)2+ 5(-3) + 4
= 9 – 15 + 4
= -2
So the correct solution of x2+ 5x + 4 = -2
(б) x 2 – 5x + 4 дает (- 3) 2 – 5 ( – 3) + 4 = 9 – 15 + 4 = – 2
Решение:
Given: x2 – 5x + 4
Now substitute the value of x = -3 in the given equation,
= (-3)2 – 5(-3) + 4
= 9 + 15 + 4
= 28
So the correct solution of x2 – 5x + 4 = 28
(c) x 2 + 5x дает (- 3) 2 + 5 (-3) = - 9 - 15 = - 24
Решение:
Given: x2 + 5x
Now substitute the value of x = -3 in the given equation,
= (-3)2 + 5(-3)
= 9 – 15
= -6
So the correct solution of x2 + 5x = -6
Вопрос 11. (у – 3) 2 = у 2 – 9
Решение:
Given: (y – 3)2 = y2 – 9
Now we check if the given statement is correct or not
Taking L.H.S:
= (y – 3)2
= y2 – 6y + 9
L.H.S ≠ R.H.S
So, the correct solution of (y – 3)2 = y2 – 6y + 9
Вопрос 12. (z + 5) 2 = z 2 + 25
Решение:
Given: (z + 5)2 = z2+ 25
Now we check if the given statement is correct or not
Taking L.H.S:
= (z + 5)2
= z2 + 10z + 25
L.H.S ≠ R.H.S
So, the correct solution of (z + 5)2 = z2 + 10z + 25
Вопрос 13. (2а + 3б) (а – б) = 2а 2 – 3б 2
Решение:
Given: (2a + 3b) (a – b) = 2a2 – 3b2
Now we check if the given statement is correct or not
Taking L.H.S:
= (2a + 3b) (a – b)
= 2a2 – 2ab + 3ab – 3b2
= 2a2 – 3b2 + ab
L.H.S ≠ R.H.S
So, the correct solution of (2a + 3b) (a – b) = 2a2 – 3b2 + ab
Вопрос 14. (а + 4) (а + 2) = а 2 + 8
Решение:
Given: (a + 4) (a + 2) = a2 + 8
Now we check if the given statement is correct or not
Taking L.H.S:
= (a + 4) (a + 2)
= a2 + 2a + 4a + 8
= a2 + 6a + 8
L.H.S ≠ R.H.S
So, the correct solution of (a + 4) (a + 2) = a2 + 6a + 8
Вопрос 15. (а – 4) (а – 2) = а 2 – 8
Решение:
Given: (a – 4) (a – 2) = a2 – 8
Now we check if the given statement is correct or not
Taking L.H.S:
= (a – 4) (a – 2)
= a2 – 2a – 4a + 8
= a2 – 6a + 8
L.H.S ≠ R.H.S
So, the correct solution of (a – 4) (a – 2) = a2 – 6a + 8
Вопрос 16. 3x 2 /3x 2 = 0
Решение:
Given: 3x2/3x2 = 0
Now we check if the given statement is correct or not
Taking L.H.S:
= 3x2/3x2
= 1
L.H.S ≠ R.H.S
So, the correct solution of 3x2/3x2 = 1
Вопрос 17. (3x 2 + 1)/(3x 2 ) = 1 + 1 = 2
Решение:
Given: (3x2 + 1)/(3x2) = 1 + 1 = 2
Now we check if the given statement is correct or not
Taking L.H.S:
= (3x2 + 1)/(3x2)
= 3x2/(3x2) + 1/(3x2)
= 1 + 1/(3x2)
L.H.S ≠ R.H.S
So, the correct solution of (3x2 + 1)/(3x2) = 1 + 1/(3x2)
Вопрос 18. (3x)/(3x + 2) = 1/2
Решение:
Given: (3x)/(3x + 2) = 1/2
Here, L.H.S ≠ R.H.S
So, the correct solution of (3x)/(3x + 2) = (3x)/(3x + 2)
Вопрос 19. 3/(4x + 3) = 1/4x
Решение:
Given: 3/(4x + 3) = 1/4x
Here, L.H.S ≠ R.H.S
So, the correct solution of 3/(4x + 3) = 3/(4x + 3)
Вопрос 20. (4x + 5)/(4x) = 5
Решение:
Given: (4x + 5)/(4x) = 5
Now we check if the given statement is correct or not
Taking L.H.S:
= (4x + 5)/(4x)
= (4x/4x) + 5/4x)
= 1 + 5/4x
L.H.S ≠ R.H.S
So, the correct solution of (4x + 5)/(4x) = 1 + 5/4x
Вопрос 21. (7x + 5)/5 = 7x
Решение:
Given: (7x + 5)/5 = 7x
Now we check if the given statement is correct or not
Taking L.H.S:
= (7x + 5)/5
= (7x/5) + 5/5)
= 7x/5 + 1
L.H.S ≠ R.H.S
So, the correct solution of (7x + 5)/5 = 7x/5 + 1