Question

if x+1/x=✓3,then find the value of x³+1/x)³​

Answer 1

Currect Question.

if , (x+1/x ) = ✓3. ,then find the value of (x³+1/x³).

Solution

Given :-

• x + 1/x = √3__________(1)

Find :-

• Value of x³ + 1/x³

Explanatiin

Using Formula

★(x + 1/x)³ = x³ + 1/x³ + 3.x².1/x + 3.x.1/x²

= x³ + 1/x³ + 3x + 3/x

= x³ + 1/x³ + 3(x + 1/x)

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we calculate here, (x³ + 1/x³)

For, this keep value by equ(1) . in this formula

==> (√3)³ = (x³ + 1/x³) + 3(√3)

==> (x³ + 1/x³) = (√3 × √3 × √3) - 3√3

==> (x³ + 1/x³) = 3√3 - 3√3 .

==> x³ + 1/x³ = 0 .

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Some Important Formula

$\star{\tt{\red{\:(a+b)^2\:=\:(a^2+b^2+2ab)}}}$

$\star{\tt{\green{\:(a-b)^2\:=\:(a^2+b^2-2ab)}}}$

$\star{\tt{\pink{\:(a^3-b^3)\:=\:(a-b)(a^2+b^2+ab)}}}$

$\star{\tt{\orange{\:(a^3+b^3)\:=\:(a+b)(a^2+b^2-ab)}}}$

$\star{\tt{\red{\:(a+b)(a-b)\:=\:(a^2-b^2)}}}$

$\star{\tt{\:(a+b)\:=\:\sqrt{(a-b)^2+4ab}}}$

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