Question

how to solve it
in brief very easy method

Answer 1

so easy just put the formula
a^2+b^2=(a+b)^2 - ab just put x+y and xy

Answer 2

it's pretty simple,

(x+y)² = x² + 2xy + y²,
now we can write it as, x²+y² = (x+y)²-2xy,

(1) Given that x+y = 12, and xy = 32, x²+y² = ?,
Substitute those values in the above formula, 
=> x²+y² = 12² - 64 = 144-64 = 80,

Now,
(2) x - 1/x = 6, Square the terms on both the sides,
=> (x - 1/x)² = 36,
=> x² + 1/x² -2(x)(1/x) = 36,
=> x² + 1/x² - 2 = 36,
=> x² + 1/x² = 38,

Therefore we got the both answers, and see it's pretty simple, The first problem answer is 80 and second problem answer is 38,

Hope you understand, Have a great day !