(3+root6)/(5 root 3-2 root 12-root 32+root 50) find value of x^4+x^2+3
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Answers
Step-by-step explanation:
→ 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 (Ans.)
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