Question

If a-b =7 and ab=30 then find the value of a,b

Answer 1

Answer-:

a-b=7--(1)

ab=30--(2)

so put 1 into 2

a=7+b

7+b×b=30

7b+b^2=30

b^2+7b-30=0

b^2+10b-3b-30=0

b(b+10)-3(b+10)=0

(b+10)(b-3)=0

so b= -10 ,b= 3

we always take a positive value

so a=7+3

a=10

Answer 2

Given: $a-b = 7$ and $ab = 30$

To find: Value of $a$ and $b$

Solution: According to the given question,

$a-b = 7$    ...(1)

⇒ $a = 7 + b$

$ab = 30$      ...(2)

Putting value of $a$ (derived from equation 1) in equation 2

⇒ $(7 + b) b= 30$

⇒ $7b + b^{2} = 30$

⇒ $b^{2} + 7b - 30=0$

Expanding the above derived equation using middle term splitting method:

⇒ $b^{2} + 10b - 3b -30 = 0$

⇒ $b(b + 10) - 3(b + 10) = 0$

⇒ $(b + 10) (b - 3) = 0$

When $(b + 10 ) = 0, b = -10$

Putting value of $b$ in equation (1)

⇒ $a - (-10) = 7$

⇒ $a + 10 = 7$

⇒ $a=-3$

When $(b-3) =0, b=3$

Putting value of $b$ in equation (1)

⇒ $a - (3) =7$

⇒ $a = 7 + 3$

⇒ $a = 10$

Hence, values of a and b are (-3, -10) and (10, 3)