Question

if x +1/x=7, then find the value of x cube +1/x cube .

Answer 1

Hey mate!!✌✌


$x + \frac{1}{x} = 7$

$(x + \frac{1}{x} ) {}^{3} = x {}^{3} + \frac{1}{x {}^{3} } + 3(x + \frac{1}{x} ) \\ \\ (7) {}^{3} = x {}^{3} + \frac{1}{x {}^{3} } + 3 \times 7 \\ \\ x {}^{3} + \frac{1}{x {}^{3} } = 343 - 21 \\ \\ x {}^{3} + \frac{1}{x {}^{3} } = 322$

Thanks for the question!

☺☺☺

Answer 2

since
x+1/x=7,

then

(x+1/x)²=x²+1/x²+2,

(7)²=x²+1/x²+2,

49-2=x²+1/x²,

then

x²+1/x²=47,


hence

(x³+1/x³)=(x+1/x)(x²+1/x²-1),

(x³+1/x³)=(7)×(47-1),

(x³+1/x³)=7×46=322