Question

(3+root6)/(5 root 3-2 root 12-root 32+root 50)​

Answer 1

Correct Question :-

if x = (3 + √6) / ( 5√3 - 2√12 - √32 + √50) , Find the value od x⁴ + x² + 3 ?

Answer :-

2√12 = 2√(2*2*3) = 2*2√3 = 4√3

√32 = √(2 * 2 * 2 * 2 * 2) = 2 * 2 √2 = 4√2

√50 = √(2 * 5 * 5) = 5√2

★Putting These values in Denominator , we get,

x = (3 + √6) / ( 5√3 - 2√12 - √32 + √50)

x = (3 + √6) / ( 5√3 - 4√3 - 4√2 + 5√2)

x = (3 + √6) / (√3 + √2)

★Rationalizing the Denominator now, we get,

x = [ (3 + √6) / (√3 + √2) ] * [ (√3 - √2) / ( √3 - √2) ]

x = [(3 + √6)*(√3 - √2)] / [(√3 + √2)(√3 - √2)]

x = [ ( 3√3 - 3√2 + √18 - √12) ] / [(√3)² - (√2)²]

x = [( 3√3 - 3√2 + √(3*3*2) - √(2*2*3) ] / ( 3 - 2 )

x = [ 3√3 - 3√2 + 3√2 - 2√3 ]

x = (3√3 - 2√3)

x = √3 .

★Putting Value of x now, we get :-

x⁴ + x² + 3

(√3)⁴ + (√3)² + 3

[(√3)²]² + 3 + 3

(3)² + 6

9 + 6

15

Your Answer = 15

Hope it helps you...