Question

if a+b=5,ab=6 and a>b find the value of 4(a^2-b^2)-a^3-b^3​

Answer 1

Answer:

1

Explanation:

a+b= 5 (given)

b= 5-a ......(I)

ab =6 (given)

a(5-a) =6 .....from(I)

5a -a^2 = 6

-a^2+5a -6=0

a^2 -5a +6 =0

a^2 -3a -2a +6 = 0

a(a-3) -2(a-3) =0

(a-3) (a-2)=0

a=3,2

when, a=3 , b=5-(3) = 2

a=2, b=5-(2)=3....... rejected because b>a

given a>b , therefore a=3,b=2)

now,

=4(a² - b²) – a³ + b³

=4(3² - 2²) – 3³ + 2³

=4(9 - 4) - 27 + 8

=4(5) - 19

= 20 - 19

= 1