Question

if x+1/x=2,then xto the power 2 +1/xto the power 2=?

Answer 1

GIVEN :-

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

TO FIND :-

$x {}^{2} + \dfrac{1}{x {}^{2} }$

SOLUTION:-

We shall do Squaring on both sides for given equation

$(x + \dfrac{1}{x} ) {}^{2} = (2) {}^{2}$

Applying (a+b)²= a² + 2ab + b²

$(x) {}^{2} + 2 \times x \times \dfrac{1}{x} + ( \dfrac{1}{x} ) { }^{2} = 4$

$x {}^{2} + \dfrac{1}{x { }^{2} } + 2 = 4$

$x {}^{2} + \dfrac{1}{x {}^{2} } = 4 - 2$

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

So, the value of x² +1/x² = 2

Know more :-

(a+ b)² = a² + b² + 2ab

( a - b )² = a² + b² - 2ab

( a + b )² + ( a - b)² = 2a² + 2b²

( a + b )² - ( a - b)² = 4ab

( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

a² + b² = ( a + b)² - 2ab

(a + b )³ = a³ + b³ + 3ab ( a + b)

( a - b)³ = a³ - b³ - 3ab ( a - b)

If a + b + c = 0 then a³ + b³ + c³ = 3abc