Question

If X+1/x=2, find the value of x^64+1/x^64
options
a. 32
b. 16
c.8
d. 2
​

Answer 1

Given :

$\bullet\ \; \; \sf x+\dfrac{1}{x}=2$

To Find :

$\bullet\ \; \; \sf Value\ of\ x^{64}+\dfrac{1}{x^{64}}\ ...(1)$

Solution :

$\sf x+\dfrac{1}{x}=2$

$:\implies \sf x=2-\dfrac{1}{x}$

$:\implies \sf x^2=2x-1$

$:\implies \sf x^2-2x+1=0$

$:\implies \sf (x-1)^2=0$

$:\implies \sf x-1=0$

$:\implies \sf \pink{x=1}\ \; \bigstar$

On sub. x value in (1) , we get ,

$\leadsto\ \sf (1)^{64}+\dfrac{1}{(1)^{64}}$

$\leadsto\ 1+\dfrac{1}{1}$

$\leadsto\ 1+1$

$\leadsto\ \green{2}\ \; \bigstar$

Option d

Answer 2

Here, as per the provided question we are asked to find the value of –

GIVEN :

• x + 1/x = 2

TO FIND :

• The value of x^64 + 1/x ^64 = ?

STEP-BY-STEP EXPLANATION :

Now, we will have to gain the value for the given question –.

→ x + 1/x = 2 (given)

→ x = 2 -1/x

→ x² = 2x - 1

→ x² - 2x + 1 = 0

→ (x - 1)² = 0

→ x-1 = 0

→ x = 1

→ (1)^64 + 1/(1)^64

→ 1 + 1/1

→ 1 + 1––›2

→2

Since, the value of 1^64+1/1^64 = 2 (d)