Question

If a-b=0.9and ab=0.36 find a+band a^2-b^3

Answer 1

given,
(a - b) = 0.9
ab = 0.36

solution :-

(a - b) = 0.9

take square both sides

(a - b)² = (0.9)² = 0.81

( a + b)² - 4ab = 0.81

( a + b)² = 0.81 + 4ab = 0.81 + 4×0.36

( a + b)²= 0.81 + 1.44 = 2.25

take square root both sides

(a + b) = ± 1.5

but ab = 0.36 >0
and ( a - b) = 0.9 >0
it means a > 0 and b > 0
so,

( a + b) = 1.5 ( answer )

again,
a + b = 1.5
a - b = 0.9

solve this equations

a = 1.2 and b = 0.3

so, a² - b³ = (1.2)² - (0.3)³

= 1.728 - 0.027
= 1.701


hence,

( a + b) = 1.5
(a² - b³) = 1.701