Question

If a-b = 0.9 and ab = 0.36; find
1) a+b (2) a²- b²​

Answer 1

Answer:

(i) We know that,

( a - b )2 = a2 - 2ab + b2

and

( a + b )2 = a2 + 2ab + b2

Rewrite the above equation, we have

( a + b )2 = a2 + b2 - 2ab + 4ab

= ( a - b )2 + 4ab ...(1)

Given that a - b = 0.9 ; ab = 0.36

Substitute the values of ( a - b ) and (ab)

in equation (1), we have

( a + b )2 = ( 0.9 )2 + 4( 0.36 )

= 0.81 + 1.44 = 2.25

⇒ a + b = ±2.25

⇒ a + b = ±1.5 ..(2)

(ii) We know that,

a2 - b2 = ( a + b )( a - b ) ....(3)

From equation (2) we have,

a + b = ±1.5

Thus equation (3) becomes,

a2 - b2 = (±1.5)(0.9) [ given a - b = 0.9 ]

⇒ a2 - b2 = ±1.35

Answer 2

Answer:

${(a + b)}^{2} = {(a - b)}^{2} + 4ab = {(0.9)}^{2} - 4 \times 0.36 = 0.81 - 1.44 = - 0.63$