The equation 4^ ( x^2 + 2) - 9.2^ ( x^2 + 2) + 8 = 0 has the solu… - Vidyadip

MCQ

The equation ${4^{({x^2} + 2)}} - {9.2^{({x^2} + 2)}} + 8 = 0$ has the solution

A
$x = 1$
B
$x = - 2$
C
$x = \sqrt 2 $
✓
(a) and (b) both

✓

Answer

Correct option: D.

(a) and (b) both

d
(d) ${4^{({x^2} + 2)}} - {9.2^{({x^2} + 2)}} + 8 = 0$

$ \Rightarrow {\left( {{2^{({x^2} + 2)}}} \right)^2} - {9.2^{({x^2} + 2)}} + 8 = 0$

Put ${2^{({x^2} + 2)}}^2 = y$. Then ${y^2} - 9y + 8 = 0$, which gives $y = 8,y = 1$.

when $y = 8\,\, \Rightarrow \,\,{2^{{x^2} + 2}} = 8$ ==> ${2^{{x^2} + 2}} = {2^3}$ ==> ${x^2} + 2 = 3$

==> ${x^2} = 1$ ==>$x = 1, - 1$.

when $y = 1$ ==> ${2^{{x^2} + 2}} = 1$ ==> ${2^{{x^2} + 2}} = {2^o}$

==> ${x^2} + 2 = 0$ ==>${x^2} = - 2$, which is not possible.

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