Question

solve question ,18,19,22,23,24,25,26

Answer 1

Answer of question number 22:

Answer 2

18) Given that x² + 1/x² =66
So, use the formula x²+1/x²=(x-1/x)²+2
It will be => 66=(x-1/x)²+2
=> 66-2 = (x-1/x)²
=> √64=x-1/x
=> 8=x-1/x

19) Given that x²+1/x²=79
So, use the formula x²+1/x²=(x+1/x)²-2
It will be => 79=(x+1/x)²-2
=>79+2=(x+1/x)²
=>√81=x+1/x
=>9=x+1/x

22) Given that a+b=10 and ab=21
So, use the formula a³+b³=(a+b)³-3ab(a+b)
=>a³+b³=10³-3×21×10
=>a³+b³=1000-630
=>a³+b³=370

23) Given that a-b=4 and ab=21
So, use the formula a³-b³=(a-b)³+3ab(a-b)
=>a³-b³=4³+3×21×4
=>a³-b³=64+252
=>a³-b³=316

24) Given that x+1/x=5
So, use the formula (x+1/x)³=x³+1/x³+3×x×1/x(x+1/x)
=>5³=x³+1/x³+3×5 {Because x and 1/x will get cancelled}
=>125=x³+1/x³+15
=>125-15=x³+1/x³
=>110=x³+1/x³

26) Given x-1/x=5
So, use the formula x³-1/x³=(x-1/x)³+3×x×1/x(x-1/x)
=> x³-1/x³=5³+3×5
=>x³-1/x³=125+15
=>x³-1/x³=140

I'm sorry that I am unable to answer question no. 25.
I hope that the others are correct.