Question

If a + b = 9 and ab = 20, find the value of (a 2 + b 2 ).

Answer 1

Answer:

Given

a+b = 9

ab = 20

therefore, a = 20/b (1)

substituting (1) in a + b =9

20/b + b = 9

or

20/b + b/1 =9/1, ( for understanding)

therefore, multiplying b in LHS and RHS,we get,

20 + b^2 =9b

therefore,

b^2 - 9b +20 =0

b^2 -5b-4b +20

b(b-5) -4(b-5)

(b-5)(b-4)

so, b=4 or 5.

then , a = 9-b

a=9-4;a=9-5

a=5 or 4.

hence proved.

hope it helps you