Question

if √57 + (12√15) = a√3 + b√5 then find the value if a = 2 and b = 3​

Answer 1

Step-by-step explanation:

I hope you understand this answer

Answer 2

The values are a=4 and b=1.

Given:

√57 + (12√15) = a√3 + b√5

To Find:

The value of the equation.

Solution:

$\frac{\sqrt[]{5}+\sqrt[]{3} }{\sqrt[]{5}-\sqrt[]{3} } =a + \sqrt[]{15} b$

Multiply and divide the equation by $\sqrt[]{5} + \sqrt[]{3}$

$\frac{\sqrt[]{5}+\sqrt[]{3} }{\sqrt[]{5}-\sqrt[]{3} }$  x $\frac{\sqrt[]{5}+\sqrt[]{3} }{\sqrt[]{5}+\sqrt[]{3} }$

=$\frac{(\sqrt[]{5}+\sqrt[]{3} )^{2} }{(\sqrt[]{5}^{2}) -(\sqrt[]{3} ^{2}) }$

=$\frac{5+2\sqrt{15}+3 }{2}$

=$\frac{8+2\sqrt{15} }{2}$

=4+$\sqrt{15}$

Hence we can infer that, a= 4 and b= 1.