CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Iota

If x-22-5|x-2...

Question

If $(x - 2)^{2} - 5 | x - 2 | + 6 = 0$ , then $x \in$

A

{0, 4}

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

B

{- 1, 5}

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

C

{- 1, 0, 4, 5}

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

D

{2, 3}

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

Open in App

Solution

The correct option is C ${- 1, 0, 4, 5}$
$(x - 2)^{2} - 5 | x - 2 | + 6 = 0 \Rightarrow | x - 2 |^{2} - 5 | x - 2 | + 6 = 0 (∵ x^{2} = | x |^{2})$

Let $| x - 2 | = t$
$\Rightarrow t^{2} - 5 t + 6 = 0$
$\Rightarrow t^{2} - 2 t - 3 t + 6 = 0$
$\Rightarrow (t - 2) (t - 3) = 0$
$\Rightarrow t = 2, 3$
$\Rightarrow | x - 2 | = 2 or | x - 2 | = 3$
$\Rightarrow x - 2 = \pm 2 or x - 2 = \pm 3$
$\Rightarrow x = 0, 4 or x = - 1, 5$
$∴ x \in {- 1, 0, 4, 5}$

Suggest Corrections

thumbs-up

0

Similar questions

(x - 2)^{2} - 5 | x - 2 | + 6 = 0

x \in

If $α, β$ are the roots of the equation $2 x^{2} + 5 x + 6 = 0$ , then find the equation whose roots are $\frac{1}{α} a n d \frac{1}{β}$ .

If $x = \sqrt{\frac{5 + 2 \sqrt{6}}{5 - 2 \sqrt{6}}}, then x^{2} (x - 10)^{2} =$

x = \sqrt{\frac{5 + 2 \sqrt{6}}{5 - 2 \sqrt{6}}}, t h e n x^{2} (x - 10)^{2} =

x^{2} - 6 | x | + 5 \leq 0

| x + 2 | < 3,

x \in

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon