Question

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

Answer 1

Solution

Given,

1. x + 1/x = √2 _______(1)

Find :-

• Value of x² + 1/x²

Explanation

Using Formula

$\dag\boxed{\underline{\tt{\orange{\:(a+b)^2\:=\:a^2+b^2+2ab}}}}$

So Follow this formula,

==> (x + 1//x)² = (√2)²

==> x² + (1/x)² + 2 × x × 1/x = √2 × √2

==> x² + 1/x² + 2 = 2

==> x² + 1/x² = 2 - 2

==> x² + 1/x² = 0

Hence

• Value of x² + 1/x² will be = 0

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Some Important Formula

★(a - b)² = a² + b² - 2ab

★(a - b)(a + b) = (a² - b²)

★ (a + b)³ = a³ + b³ + 3ab(a + b)

★ (a - b)³ = a³ - b³ + 3ab(a - b)

★(a³ + b³) = (a + b)(a² -ab+b²)

★(a³ - b³) = (a - b)(a² + ab+b²)

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