Question

X+1/x =3 then x2+1/x2 is equal to

Answer 1

Answer:

x² + 1/x² = 7

Step-by-step explanation:

Given that :

• x + 1/x = 3

To find:

• x² + 1/x²

Solution:

$\implies \tt x + \frac{1}{x} = 3 \\ \\ \bf \underline{ On \: squaring \: both \: sides :} \\ \\ \implies \tt \left( x + \frac{1}{x} \right)^{2} = (3) {}^{2} \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } + 2 \: . x\: . \frac{1}{x} = 9 \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ \\ \boxed{ \red{ \bf \therefore \: {x}^{2} + \frac{1}{ {x}^{2} } = 7}}$

Hence, the answer is 7.

Answer 2

Step-by-step explanation:

X+1/x = 3

squaring both side

(X+1/x) power 2 = (3) power 2.

(x) power 2 +( 1/x) power 2 + 2(x*1/x) = 9

(x) power 2 +(1/x) power 2 + 2 = 9

(x) power2 +(1/x) power = 7

hence, x2+1/x2 =7