Question

if a+1/a=1,then find the value of a^3+1​

Answer 1

hope it helps u mate ...

Answer 2

$\huge{\frak{\green{QuEsTion}}}$

$\bf if a+\frac{1}{a}=1 ,\\\bf then\:find\:the\:value\:of\:a^3+1.$

$\huge{\frak{\green{SoluTion}}}$

given that ,

$\bf a + \frac{1}{a}=1\\\\\bf \frac{a^2+1}{a}=1\\\\\bf a^2+1=a\\\\\boxed{\bf{a^2-a+1=0..........eqn(1)}}$

to find

$\bf a^3 + 1 = a^3+(1)^3\\ \\ \bf using\:identity\:\\\bf{ x^3+y^3 = (x+y)(x^2-xy+y^2)}\\\\\bf a^3+1=(a+1)(a^2-a+1)\\\\\bf (using\:eqn\:(1))\\\\\bf a^3+1 = (a+1)(0) = 0\\\\\boxed{\bf therefore\:\: a^3+1=0}$