Question

x2+ 1/x2 if x+1/x=3​

Answer 1

Answer

x² + ¹/x² = 7

Given

$\bullet \;\; \rm x+\dfrac{1}{x}=3$

To Find

$\bullet \;\; \rm x^2+\dfrac{1}{x^2} = ?$

Formula Used

$\bullet \;\; \rm (a+b)^2=a^2+b^2+2ab$

Solution

$\rm x+\dfrac{1}{x}=3$

Squaring on both sides , we get ,

$\to\ \rm \bigg(x+\dfrac{1}{x}\bigg)^2=(3)^2\\\\\to\ \rm x^2+\dfrac{1}{x^2}+2.x.\dfrac{1}{x}=9\\\\\to\ \rm x^2+\dfrac{1}{x^2}+2=9\\\\\to\ \rm x^2+\dfrac{1}{x^2}=9-2\\\\\to\ \rm{\pink{x^2+\dfrac{1}{x^2}=7\ \; \bigstar}}$

Answer 2

$\huge{\underline{\underline{\bf{\red{\:\:Given\:\:}}}}}$

• $\sf\orange{x \ + \ \dfrac{1}{x} \ = \ 3}$

$\huge{\underline{\underline{\bf{\green{\:\:To \ Find\:\:}}}}}$

• $\sf\orange{x^2 \ + \ \dfrac{1}{x^2} \ = \ ?}$

$\large{\underline{\underline{\bf{\purple{\:\:Formula \ to \ be \ used\:\:}}}}}$

• $\sf\orange{(a \ + \ b)^2 \ = \ a^2 \ + \ b^2 \ + \ 2ab}$

$\huge{\underline{\underline{\bf{\pink{\:\: Solution\:\:}}}}}$

$\mapsto \:\:\sf\blue{x \ + \ \dfrac{1}{x} \ = \ 3}$

$\bf\underline\red{Squaring \ on \ both \ sides}$

$\mapsto \:\:\sf\blue{ \Bigg( x \ + \ \dfrac{1}{x} \Bigg) ^2 \ = \ (3)^2}$

$\mapsto \:\:\sf\blue{x^2 \ + \ \dfrac{1}{x^2} \ + \ 2 \ . \ x \ . \ \dfrac{1}{x} \ = \ 9}$

$\mapsto \:\:\sf\blue{x^2 \ + \ \dfrac{1}{x^2} \ + \ 2 \ = \ 9}$

$\mapsto \:\:\sf\blue{x^2 \ + \ \dfrac{1}{x^2} \ = \ 9 \ - \ 2}$

$\mapsto \:\:\sf\blue{x^2 \ + \ \dfrac{1}{x^2} \ = \ 7}$

★ ${\boxed{\bf{\red{Hence, \ x^2 \ + \ \dfrac{1}{x^2} \ = \ 7}}}}$