Question

please solve this question​

Answer 1

Answer:

The answer is $a=5,b=2$

Step-by-step explanation:

   $\frac{\sqrt 3+\sqrt 2}{\sqrt 3-\sqrt 2}$ , given expression

$=\frac{\sqrt 3+\sqrt 2}{\sqrt 3-\sqrt 2}\times \frac{\sqrt 3+\sqrt 2}{\sqrt 3+\sqrt 2}$, rationalize the denominator

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

$=\frac{(\sqrt3)^2+(\sqrt 2)^2+2\sqrt 3\times \sqrt 2}{3-2}$, using $(a+b)^2=a^2+b^2+2ab$

$=\frac{3+2+2\sqrt {3\times 2}}{1}\\=5+2\sqrt 6=a+b\sqrt 6\\\therefore a=5, b=2$

Answer 2

Question:

If (√3 + √2)/(√3 - √2) = a + b√6 then find the value of a and b.

Answer:

a = 5, b = 2

Step-by-step explanation:

Giv: (√3 + √2)/(√3 - √2) = a + b√6. We need to find out the value of a and b.

So, let's start by rationalising the denominator. While rationalising we use the opposite sign given in denominator and then multiply & divide that with the given value.

→ (√3 + √2)/(√3 - √2) × (√3 + √2)/(√3 + √2)

→ [(√3 + √2)(√3 + √2)]/[(√3 - √2)(√3 + √2)]

Used identity: (a + b)(a - b) = a² - b²

As, root means 1/2 and square of root means 2 × 1/2 which means 1. Therefore,

→ [√3(√3 + √2) + √2(√3 + √2)]/(3 - 2)

→ (3 + √6 + √6 + 2)/1

→ 5 + 2√6

On comparing 5 + 2√6 with a + b√6 we get,

→ a = 5 and b = 2