Question

If a + b = 7 and ab = 12, then the value of (a^2-b^2).

Answer 1

Given that

aa ++ b=7b=7  …….. (1)

and

ab=12ab=12 …….. (2)

We have to find the value of

a2+b2−aba2+b2−ab

From (1) ,

a=7−ba=7−b …….. (3)

From (2) & (3) , we get

(7−b)b=12(7−b)b=12

=>7b−b2=12=>7b−b2=12

=>b2−7b+12=0=>b2−7b+12=0

=>b2−3b−4b+12=0=>b2−3b−4b+12=0

=>b(b−3)−4(b−3)=0=>b(b−3)−4(b−3)=0

=>(b−3)(b−4)=0=>(b−3)(b−4)=0

=>b=3,4=>b=3,4

If b=3,a=7–3=4b=3,a=7–3=4

Therefore,a2+b2−aba2+b2−ab

=42+32−4(3)=42+32−4(3)

=16+9−12=16+9−12

=13.=13.

If b=4,a=7−4=3b=4,a=7−4=3

Therefore,

a2+b2−aba2+b2−ab

=32+42−3(4)=32+42−3(4)

=9+16−12=9+16−12

=13=13

Hence , a2+b2−ab=13.a2+b2−ab=13.

Answer 2

Answer:

given

a+b=7 and ab=12

if a+b=7

 a  = 7-b

ab = (7-b)b

(7-b)b = 12

7b-b²  = 12

b²-7b+12 = 0

b²-3b-4b+12=0

b(b-3)-4(b-3) = 0

(b-4)(b-3)    = 0

b= 4,3

a = (7-b) = (7-4)    or (7-3)

              = 3        or  4

b=3  or  4

a = 4  or 3

a²-b²  = 4²-3²    or  3²-4²

          =16-9   or    9-16

           = 7       or    -7

a²-b² = 7 or (-7)