Question

if x+1/x=√5 find the value of x^2+1/x^2​

Answer 1

Answer:

3

Step-by-step explanation:

x+1/x =√5

x²+1/x² = (x+1/x)²-2 = 5-2 = 3

Answer 2

Answer :

$\sf{x^2+\dfrac{1}{x^2}=3}$

Step-by-step explanation :

$\sf{x+\dfrac{1}{x}=\sqrt{5}}$

• Squaring on Both Sides

$\to\sf{\left(x+\dfrac{1}{x}\right)^2=(\sqrt{5})^2}$

• Apply Algebraic Identify : $\sf{(a+b)^2=a^2+b^2+2ab}$

$\to\sf{x^2+\dfrac{1^2}{x^2}+2\times x\times \dfrac{1}{x}=(\sqrt{5})^2}$

• We know $\sf{(\sqrt{a})^2=a}$

$\to\sf{x^2+\dfrac{1}{x^2}+2=5}$

• Subtracting 2 from both Sides

$\to\sf{x^2+\dfrac{1}{x^2}+2-2=5-2}$

$\boxed{\to\sf{x^2+\dfrac{1}{x^2}=3}}$