if x+1byx=2 then find the value of xto the power 3+1by xto the power 3
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Step-by-step explanation:
x⁴ + 1/x⁴ = 47
Add 2 both sides :
= x⁴ + 1/x⁴ + 2 = 47 + 2
= x⁴ + 1/x⁴ + 2.x⁴.1/x⁴ + 2 = 49
Using ( a² + b² + 2 ab ) as ( a + b )²
= ( x² + 1/x² )² = 49
Take square root both sides
= x² + 1/x² = 7
Add 2 both sides again :
= x² + 1/x² + 2.x.1/x = 7 + 2
Using a² + b² + 2 ab = ( a + b )²
= ( x + 1/x )² = 9
Taking square root both sides
= x + 1/x = 3
Cube both sides
= ( x + 1/x )³ = 3³
= x³ + 1/x³ + 3 ( x + 1/x ) = 27
= x³ + 1/x³ + 3.3 = 27
= x³ + 1/x³ + 9 = 27
= x³ + 1/x³ = 27 - 9
= x³ + 1/x³ = 18
The value will be 18 .
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