Question

if a-b=3 and ab=4,find a³-b²​

Answer 1

Answer:

15

Step-by-step explanation:

We have two equations,

a-b =3     --(1)

ab=4       --(2)

now solve for a and b,

from eq. (1) we get:  a=3+b      --(3)

from eq. (2) we get a=4/b        --(4)

Equate equation a from (3) and (4),

we get: 3+b = 4/b

        => 3b + b^2 =4

        => b^2 +3b -4 = 0

Solving the above quadratic equation we find the roots of b.. ie,  b=1 and-4.

Since -4 is negative lets assume b =1, substituting the value of b in equation (2) we get the value of a.

Therefore, a=4 and b=1.

Now we know the values a and b, substitute in  a^3-b^2

ie, (4)^3  - (1)^2

=> 16 - 1

=> 15