Which of the following is the reduced form of the equation $(x - 2)^{3}$ = $(2 x - 1)^{2} + x^{3}$ ?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D

$(x - 2)^{3}$ = $(2 x - 1)^{2} + x^{3}$

$\to$ $x^{3} - 6 x^{2} + 12 x - 8 = 4 x^{2} - 4 x + 1 + x^{3}$

$\to$ $10 x^{2} - 16 x + 9 = 0$

Suggest Corrections

Similar questions

Which of the following is the reduced form of the equation $(2 x - 1)^{2} = x^{2} + 2$ ?

Which of the following is reduced form of the equation $(2 x - 1)^{2}$ = $x^{2}$ + 2?

Q. The reduced form of

(2 x - 1)^{2} = x^{2} + 2

is NOT a quadratic equation.

Check whether the following are quadratic equations :
(i) ${(x + 1)}^{2} = 2 (x - 3)$
(ii) $x^{2} - 2 x = (- 2) (3 - x)$
(iii) $(x - 2) (x + 1) = (x - 1) (x + 3)$
(iv) $(x - 3) (2 x + 1) = x (x + 5)$
(v) $(2 x - 1) (x - 3) = (x + 5) (x - 1)$
(vi) $x^{2} + 3 x + 1 = {(x - 2)}^{2}$
(vii) ${(x + 2)}^{3} = 2 x (x^{2} - 1)$
(viii) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

Q. Is the following equation a quadratic equation?

(x + 2)^{3} = x^{3} - 4

Join BYJU'S Learning Program

Which of the following is the reduced form of the equation (x−2)3 = (2x−1)2+x3 ?

The correct option is D (x−2)3 = (2x−1)2+x3 → x3−6x2+12x–8=4x2−4x+1+x3 → 10x2–16x+9=0

Which of the following is the reduced form of the equation $(x - 2)^{3}$ = $(2 x - 1)^{2} + x^{3}$ ?

The correct option is D

$(x - 2)^{3}$ = $(2 x - 1)^{2} + x^{3}$

$\to$ $x^{3} - 6 x^{2} + 12 x - 8 = 4 x^{2} - 4 x + 1 + x^{3}$

$\to$ $10 x^{2} - 16 x + 9 = 0$