Question

if a2+b2= 20 and ab=8 find the value of a+b and a-b​

Answer 1

Answer:

a + b = 6

a-b = 2

Step-by-step explanation:

$a^{2} + b^{2} = 20\\ab = 8\\\\a^{2} + b^{2} = 2 X ab = (a+b)^{2} \\ 20 + 16 = (a+b)^{2}\\ 36 = (a+b)^{2}\\ a+b = 6$

$a2 + b2 - 2ab = (a-b)2\\\\\\20- 16 = (a-b)2\\4=(a-b)2\\a-b = 2$

Answer 2

Answer:

GIVEN:

a²+b²=20

ab=8

REQUIRED TO FIND:

a+b and a-b.

PROOF:

Let a+b=x.

Square on both sides.

⇒(a+b)²=x²

⇒a²+b²+2ab=x²

Substitute the values of a²+b²=20 and ab=8. this gives us:

⇒20+2×8=x²

⇒20+16=x²

⇒36=x²

⇒x=√36

⇒x=6.

Thus, the value of a+b is 6.

Let a-b=y.

Square on both sides.

⇒(a-b)²=y²

⇒a²+b²-2ab=y²

Substitute the values of a²+b²=20 and ab=8. this gives us:

⇒20-2×8=y²

⇒20-16=y²

⇒4=y²

⇒y=√4

⇒y=2.

Thus, the value of a-b is 2.

HOPE THIS HELPS :D