Question

if 8x/2x^2+7x-2=1 ,x>0 then find
x^3+1/x^3​

Answer 1

Step-by-step explanation:

x^3+1/x^3=5/8√17

x-1/X=1/2

x+1/X=√17/2

so

x^3+1/x^3=5/8√17

Answer 2

value of x³ + 1/x³ = 5√17/8

your question is .... 8x/(2x² + 7x - 2) = 1 then we have to find x³ + 1/x³

let's resolve, 8x/(2x² + 7x - 2) = 1

⇒8x = 2x² + 7x - 2

⇒2x² + 7x - 2 - 8x = 0

⇒2x² - x - 2 = 0

⇒(2x² - x - 2)/x = 0/x

⇒2x - 1 - 2/x = 0

⇒2(x - 1/x) = 1

⇒x - 1/x = 1/2

⇒(x + 1/x)² = (x - 1/x)² + 4x.1/x

= (1/2)² + 4

= 1/4 + 4

= 17/4

x + 1/x = √17/2

now, x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x)

= 17√17/8 - 3√17/2

= 17√17 - 12√17/8

= 5√17/8

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