Question

if a+b=7 abd ab=10, find thvalue of a-b

Answer 1

Answer:

The value of a-b is 3 or -3.

Step-by-step explanation:

Given, a + b = 7                                equation(1)

   and a . b = 10                                equation(2)

from equation(1),

           b = 7 - a

on putting the value of b in equation(2),

           a . (7 - a) = 10

           7a - $a^{2}$ = 10

            $a^{2}$ - 7a + 10 = 0

            $a^{2}$ - 5a - 2a + 10 = 0

            a(a - 5) - 2(a - 5) = 0

            (a - 2)(a - 5) = 0

            a = 2, 5

On putting the value of a in equation(1)

            b = 7 - 2     ,    b = 7 - 5

            b = 5          ,    b = 2

The value of a - b = 5 - 2 = 3

                 or a - b = 2 - 5 = -3

Thus, the value of a - b is 3 or -3.