Question

simplifyroot 13 -root 11 /root 13 +root 11 + root 13 +root 11/root 13 -root 11

Answer 1

GIVEN :

The expression is $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$ and simplify the given expression.

TO SIMPLIFY :

The given expression $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$ and get the value of the expression.

SOLUTION :

Given expression is $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$

Now solving the given expression as below:

$\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$

$=\frac{(\sqrt{13}-\sqrt{11})(\sqrt{13}-\sqrt{11})+(\sqrt{13}+\sqrt{11})(\sqrt{13}+\sqrt{11})}{(\sqrt{13}+\sqrt{11})(\sqrt{13}-\sqrt{11})}$

By using the algebraic identities :

$(a+b)^2=a^2+2ab+b^2$

$(a-b)^2=a^2-2ab+b^2$ and

$(a+b)(a-b)=a^2-b^2$

$=\frac{(\sqrt{13}-\sqrt{11})^2+(\sqrt{13}+\sqrt{11})^2}{(\sqrt{13})^2-(\sqrt{11})^2}$

$=\frac{(\sqrt{13})^2-2(\sqrt{13})(\sqrt{11})+(\sqrt{11})^2+(\sqrt{13})^2+2(\sqrt{13})(\sqrt{11})+(\sqrt{11})^2}{13-11}$

$=\frac{13+11+13+11}{2}$

By adding the like terms we get,

$=\frac{48}{2}$

$=24$

∴ $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}=24$

∴ the given expression $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$ is simplified into the value is 24.

Answer 2

Answer:

24

Step-by-step explanation:

√13-√11/√13+√11+√13+√11/√13-√11

=(√13-√11)²+(√13+√11)²/(√13+√11)(√13-√11)

=[(√13)²-2(√13)(√11)+(√11)²]+[(√13)²+2(√13)(√11)+(√11)²]/(√13)²-(√11)²

=[13-2√143+11]+[13+2√143+11]/13-11

=24-2√143+24+2√143/2

=48/2

=24