Question

(a) If a - b = 5 and ab = 75 find the value of a2 + b2.
(b) If x - y = 5 and xy = 50, find the value of x2 + y2.
(C) If 2x – 3y = 2 and xy = 8 then find the value of 4x2 +9y2.
(d) If 4x - 5y = 6 and xy = 8 then find the value of 16x2 + 25y2​

Answer 1

Step-by-step explanation:

a. (a-b)^2=a^2+b^2-2(ab)

5^2=a^2+b^2-2(75)

25=a^2+b^2-150

a^2+b^2=175

b. 5^2=a^2+b^2-2(50)

25=a^2+b^2-100

a^2+b^2=125

c. (2x-3y)^2=4x^2+9y^2-2(8)

2^2=4x^2+9y^2-16

4+16=4x^2+9y^2

4x^2+9y^2=20

d. (4x-5y)^2=16x^2+25y^2-2(8)

6^2=16x^2+25y^2-16

16x^2+25y^2=36+16

16x^2+25y^2=52