Question

if x^2+1/x^2=34 then find the value of x+1/x

Answer 1

Answer:

Step-by-step explanation:

x²+1/x²=34

Adding 2 to both sides we get,

x²+1/x²+2=36

(x)²+(1/x)²+2.x.1/x=(±6)²

(x+1/x)²=(±6)²

x+1/x=±6

Answer 2

Answer:

± 6

Step-by-step explanation:

Given that;

$\tt {x}^{2} + \dfrac{1}{ {x}^{2} } = 34$

On adding 2 both sides ;

$\tt x^{2} + \frac{1}{ {x}^{2}} + 2 = 34 + 2 \\ \\ \tt {x}^{2} + \frac{1}{ {x}^{2} } + 2 \: . \: x \: . \: \frac{1}{x} = 36 \\ \\ \tt (x + \frac{1}{x} )^{2} = 36 \\ \\ \tt x + \frac{1}{x} = \pm \sqrt{36} \\ \\ \tt x + \frac{1}{x} =\pm 6$

Hence, the answer is ±6.

_______________________

★ Identity Used -

• (a + b)² = a² + 2ab + b²