FORMULA FOR A SQUARE PLUS B SQUARE

Problem 1 :

If p + q = 12 and pq = 22, then find p² + q².

Solution :

p + q = 12 and pq = 22

Write the formula for a² + b² = (a + b)² - 2ab

p² + q² = (p + q)² - 2pq

= (12)² - 2(22)

= 144 – 44

p² + q² = 100

Problem 2 :

If a + b = 25 and a² + b² = 225, then find ab.

Solution :

a + b = 25 and a² + b² = 225

Write the formula for a² + b² = (a + b)² - 2ab

225 = (25)² - 2ab

225 = 625 – 2ab

2ab = 625 – 225

2ab = 400

ab = 400 / 2

ab = 200

Problem 3 :

If x – y = 13 and xy = 28, then find x² + y².

Solution :

x – y = 13 and xy = 28

Write the formula for a² + b² = (a - b)² + 2ab

x² + y² = (x - y)² + 2xy

= (13)² + 2(28)

= 169 + 56

x² + y² = 225

Problem 4 :

If m - n = 16 and m² + n² = 400, then find mn.

Solution :

m - n = 16 and m² + n² = 400

Write the formula for a² + b² = (a - b)² + 2ab

m² + n² = (m - n)² + 2mn

400 = (16)² - 2mn

400 = 256 – 2mn

2mn = 400 – 256

2mn = 144

mn = 144 / 2

mn = 72

Problem 5 :

If a² + b² = 74 and ab = 35, then find a + b.

Solution :

a² + b² = 74 and ab = 35

Write the formula for a² + b² = (a + b)² - 2ab

74 = (a + b)² - 2(35)

74 = (a + b)² - 70

(a + b)² = 74 – 70

(a + b)² = 4

a + b = 2