The number of real roots of x-14-x-14-16 is-A- 0B- NoneC- 1D- 2

The correct option is D 2 (x 1)^4 + (x + 1)^4 = 16. 2 { x^4 + 6x^2 + 1 } = 16 x^4 + 6x^2 7 = 0 ( x^2 1 ) ( x^2 + 7 ) = 0 x = ± 1 are the only real so ...

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

Byju's Answer

Standard XII

Mathematics

Drawing a Graph

The number of...

Question

The number of real roots of $(x - 1)^{4} + (x + 1)^{4} = 16$ is :

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

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

None

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

Open in App

Solution

The correct option is B
2

$(x - 1)^{4} + (x + 1)^{4} = 16.$

$2 {x^{4} + 6 x^{2} + 1} = 16$

$x^{4} + 6 x^{2} - 7 = 0$

$(x^{2} - 1) (x^{2} + 7) = 0$

$x = \pm 1$ are the only real solutions.

Suggest Corrections

Similar questions

Q. The number of real roots of the equation

x^{2} - 3 x + 5 = 0

is:

Sum of the real roots in the equation $x^{2} | x | - 17 x^{2} + 95 | x | - 175$ = 0 is:

The number of real solutions of the equation $x^{2} + 3 | x | + 2$ =0 is:

Q. Let

α, β

are the roots of the equation

2 x^{2} - 3 x - 7 = 0

, then the quadratic equation whose roots are

\frac{α}{β}

and

\frac{β}{α}

Q. The roots of the equation

2 x^{2} - 7 x + 14 = 0

are ___________

Join BYJU'S Learning Program

The number of real roots of (x−1)4+(x+1)4=16 is :

The correct option is B 2 (x−1)4+(x+1)4=16. 2{x4+6x2+1}=16 x4+6x2−7=0 (x2−1)(x2+7)=0 x=± 1 are the only real solutions.

The number of real roots of $(x - 1)^{4} + (x + 1)^{4} = 16$ is :

The correct option is B
2

$(x - 1)^{4} + (x + 1)^{4} = 16.$

$2 {x^{4} + 6 x^{2} + 1} = 16$

$x^{4} + 6 x^{2} - 7 = 0$

$(x^{2} - 1) (x^{2} + 7) = 0$

$x = \pm 1$ are the only real solutions.