Question

If a+b=10 and ab=20 find the value of a2+b2 and (a-b)whole square

Answer 1

Hey There!



Here, we are given two things:
a + b = 10

ab = 20


Now, we can find the other things as follows:

$(a+b)^2 = a^2+2ab+b^2 \\ \\ \implies 10^2 = a^2+2\times 20 + b^2 \\ \\ \implies 100 = a^2 + 40 + b^2 \\ \\ \implies \boxed{a^2+b^2=60} \\ \\ \\ \\ \\ (a-b)^2 = a^2+b^2-2ab \\ \\ \implies (a-b)^2 = 60 - 2\times 20 \\ \\ \implies \boxed{(a-b)^2=20}$


Hope it helps
Purva
Brainly Community

Answer 2

Answer :-

a² + b² = 60

(a - b)² = 20

Solution :-

i) Finding a² + b²

We know that

(a + b)² = a² + b² + 2ab

Here

• a + b = 10

• ab = 20

By substituting the values

⇒ (10)² = a² + b² + 2(20)

⇒ 100 = a² + b² + 40

⇒ 100 - 40 = a² + b²

⇒ a² + b² = 60

ii) Finding (a - b)²

We know that

(a + b)² = (a - b)² + 4ab

Here

• a + b = 10

• ab = 20

By substituting the values

⇒ (10)² = (a - b)² + 4(20)

⇒ 100 = (a - b)² + 80

⇒ 100 - 80 = (a - b)²

⇒ 20 = (a - b)²

⇒ (a - b)² = 20