Question

if a/b+b/a=1,(a and b is not equal to 0) ,then what is value of a cube + b cube

plz solve this ...

Answer 1

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} ) \\ \frac{a}{b} + \frac{b}{ a} = 1 \\ \frac{ {a}^{2} + {b}^{2} }{ab} = 1 \\ {a}^{2} + {b}^{2} = ab \\ {a}^{2} - ab + {b}^{2} = 0$
place this value into standard identity
a^3+ b^3=0 ans