Question

If a+b=10 and a-b=6,then find the value of (a²+b²)

Answer 1

Step-by-step explanation:

given,

a+b=10.............( eqn 1)

a-b=6................(eqn 2)

adding eqn1 and eqn2

a+b=10

a-b=6

______

2a=16

a=16/2

a=8

putting the value of a in eqn 1

a+b=10

8+b=10

b=10-8

b=2

now,

(a²+b²)= 64+4=68

Answer 2

68

Step-by-step explanation:

Sets of equations:

1) a + b = 10

2) a - b = 6

Make 'a' the subject:

1) a = 10 - b --- equation 1

2) a = 6 + b --- equation 2

Solve them by substituting:

⇒ 10 - b = 6 + b

⇒ -b - b = 6 - 10

⇒ -2b = -4

⇒ b = 2

Find value of 'a', a = 10 - b, a = 10 - 2 = 8

Then find (a²+b²), by inserting a = 8, b = 2,

⇒ ((8)²+(2)²) = 64 + 4 = 68