Question

if x = √3+√2/√3-√2 then find the value of x²​

Answer 1

Answer:

x= √3+√2/√3-√2

x²= (√3+√2/√3-√2)²

using

• (a-b)²=a²+b²-2ab
• (a+b)²=a²+b²+2ab

x²=(√3)²+(√2)²+2(√3)(√2)/ (√3)²+(√2)²-2(√3)(√2)

3+2+2√6/3+2-2√6

5+2√6/5-2√6

Rationalising the denominator

(5+2√6)²/(5-2√6)(5+2√6)

using

• (a+b)²=a²+b²+2ab
• (a-b)(a+b)= a²-b²

(5)²+(2√6)²+2(5)(2√6) / (5)²-(2√6)²

25+24+20√6 / 25-24

x²=48+20√6

Answer 2

Answer:

The value of given expression is

${x}^{2} = 49 + 20 \sqrt{6}$

Step-by-step explanation:

The given variable is

$x = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} }$

We shall rationalise the number first by multiplying and dividing the number with rationalising factor of denominator.Performing the operation gives

$x = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = \frac{( \sqrt{3} + \sqrt{2} ) {}^{2} }{( \sqrt{3} ) {}^{2} - {( \sqrt{2} )}^{2} } \\ = \frac{5 + 2 \sqrt{6} }{3 - 2} = 5 + 2 \sqrt{6}$

Squaring it will result as shown below

${x}^{2} = {(5 + 2 \sqrt{6} )}^{2} \\ = {5}^{2} + (2 \sqrt{6} ) {}^{2} + 2(5)(2 \sqrt{6} ) \\ = 25 + 24 + 20 \sqrt{6} \\ = 49 + 20 \sqrt{6}$

Hence the value of given expression is

${x}^{2} = 49 + 20 \sqrt{6}$

#SPJ2