Question

if √5+√3/√5-√3=a+b√15 then find the value of (a+b)a

Answer 1

Answer:

The value of (a+b)a is 20.

Step-by-step explanation:

The given equation is

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

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

$\frac{(\sqrt{5}+\sqrt{3})^2}{(\sqrt{5})^2-(\sqrt{3})^2}=a+b\sqrt{15}$

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

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

$4+\sqrt{15}=a+b\sqrt{15}$

On comparing both sides.

$a=4$

$b=1$

The value of (a+b)a is

$(a+b)a=(4+1)4=5\times 4=20$

Therefore the value of (a+b)a is 20.

Answer 2

20 is the value of (a + b)a

Step-by-step explanation:

Given that,

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

To find,

a = ?

b = ?

Multiplying and dividing the given equation by $\sqrt{5} + \sqrt{3}$

⇒ $\frac{\sqrt{5} + \sqrt{3} }{\sqrt{5} - \sqrt{3} } * \frac{\sqrt{5} + \sqrt{3} }{\sqrt{5} + \sqrt{3} }$

⇒ $\frac{(\sqrt{5} + \sqrt{3})^{2} }{(\sqrt{5})^2 - (\sqrt{3})^2 }$

⇒ $\frac{(\sqrt{5})^2 + 2.\sqrt{5} . \sqrt{3} +(\sqrt{3})^2 }{5-2}$

⇒  $\frac{5 + 2\sqrt{15} + 3}{2}$

⇒ $\frac{8 + 2 \sqrt{15} }{2}$

⇒ 4 + $\sqrt{15}$ = a+b√15

∵ a = 4 and b = 1

Thus, (a + b)a = (4 + 1)4 = 20

Learn more: find the value of a

brainly.in/question/17520931