Question

if 3+root 8/3-root 8 + 3-root 8 / 3+ root 8 =a+b root 2 find a and b

Answer 1

hope it helps u ...✌✌✌✌✌✌✌

Answer 2

The value of a and b is $a=b=\frac{17\sqrt{2}}{4}$.

Step-by-step explanation:

Given : Expression $\frac{3+\sqrt{8}}{3-\sqrt{8}}+\frac{3-\sqrt{8}}{3+\sqrt{8}}=(a+b)\sqrt2$

To find : The value of a and b ?

Solution :

$\frac{(3+\sqrt{8})(3+\sqrt{8})+(3-\sqrt{8})(3-\sqrt{8})}{(3-\sqrt{8})(3+\sqrt{8})}=a+b\sqrt2$

$\frac{(3+\sqrt{8})^2+(3-\sqrt{8})^2}{(3)^2-(\sqrt{8})^2}=a+b\sqrt2$

$\frac{9+8+6\sqrt8+9+8-6\sqrt8}{9-8}=a+b\sqrt2$

$\frac{34}{1}=a+b\sqrt2$

$34=a+b\sqrt2$

$17+17=(a+b)\sqrt2$

Multiply and divide by 4,

$(\frac{17\sqrt{2}}{4}+\frac{17\sqrt{2}}{4})\sqrt2=(a+b)\sqrt2$

The value of a and b is $a=b=\frac{17\sqrt{2}}{4}$.

#Learn more

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