Question

If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a² - b².

Answer 1

(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 = `+- sqrt2.25`
⇒ 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