Question

if a+b=7and ab=10,find a-b​

Answer 1

Answer:

(a+b)^2= (a-b)^2+ 4ab

or, (a-b)^2=49-40

so,,,, a-b=+3 .....

Answer 2

Given, (a+b)=7(a+b)=7, ab=10ab=10

Squaring both sides

\Rightarrow (a+b)^2=7^2⇒(a+b)

2

=7

2

\Rightarrow a^2+b^2+2ab=49⇒a

2

+b

2

+2ab=49

\Rightarrow a^2+b^2=49-2(10)⇒a

2

+b

2

=49−2(10)

\Rightarrow a^2+b^2=29⇒a

2

+b

2

=29

Now,

(a-b)^2=a^2+b^2-2ab(a−b)

2

=a

2

+b

2

−2ab

=29-2(10)=29−2(10)

=29-20=29−20

=9=9

\therefore a-b=\sqrt{9}∴a−b=

9

=\pm {3}=±3