Question

If a/b + b/a = 1, (a , b are not equal to zero) , Find the value of a^3 + b^3 ; (where ^ means power or exponent) *
-1
0
1
1/2​

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

Given :-

$\sf{\dfrac{a}{b} + \dfrac{b}{a} = 1}$

a , b ≠ 0

To Find :-

$\sf{(a^{3} + b^{3}) = ?}$

Solution :-

$\sf{\dfrac{a}{b} + \dfrac{b}{a} = 1}$

Here ,

Let :- $\sf{\dfrac{a}{b} = x}$

$\sf{then \: ,}$

$\sf{\dfrac{b}{a} =\dfrac{1}{x}}$

Now ,

$\sf{x + \dfrac{1}{x} = 1}$

Doing square both side -

$\sf{x^{2} + \dfrac{1}{x^{2}} + 2 = 1}$

$\sf{x^{2} + \dfrac{1}{x^{2}} = -1}$

$\sf{x(x^{2} + \dfrac{1}{x^{2}}) = -x}$

$\sf{x^{3} + \dfrac{1}{x} = -x}$

$\sf{x^{3} = -(x + \dfrac{1}{x})}$

$\sf{ x^{3} = -1}$

means ,

$\sf{\dfrac{a^{3}}{b^{3}} = -1}$

$\sf{a^{3} = - b^{3}}$

$\sf{a^{3} + b^{3} = 0}$

Result :-

$\sf{value \: of \: (a^{3} + b^{3}) \: is \: \: 0 . }$