Question

If x*3+1/x*3=110 find the value of x-1/x. The answer of this question is 5

Answer 1

Heya..!!!


X³ + 1/x³ = 110


We know that:-


(a + b)³ = a³ + b³ + 3ab(a + b)

Here, a = x , b = 1/x

⇒(x + 1/x)³ = x³ + 1/x³ + 3*x *1/x (x + 1/x)

∴ [ let (x + 1/x) = p]

⇒(p)³ = 110 + 3p
∴ [ x³ + 1/x³ = 110 ]

⇒p³ - 3p - 100 = 0

⇒p³ + 0p² - (25 - 22)p - 110 = 0
∴[ 0 can be written as 5 - 5 = 0 ]

⇒p³ + 5p² - 5p² - 25p + 22p - 110 = 0

⇒ P³ + 5p² + 22p - 5p² - 25p - 110 = 0

⇒p(p² + 5p + 22) - 5(p² + 5p + 22) = 0

⇒(p² + 5p + 22) (p - 5) = 0

⇒(p - 5) = 0 or (p² + 5p + 22) = 0

⇒p = 5 or (p² + 5p + 22) = 0 ∴ [ neglect]

now p = 5

Hence,

X + 1/x = 5


$VERIFICATION:-$

⇒(x + 1/x)³ =( x³ + 1/x³) + 3*x *1/x (x + 1/x)
∴ [ x³ + 1/x³ = 110 ]

⇒ (5)³ = 110 + 3(5)

⇒125 = 110 + 15

⇒125 = 125



I HOPE ITS HELP YOU,