Question

If AB x B = 9B then the values of A and B are _____________.

Answer 1

Answer:

Given, a + b = 9 and ab = 18

a + b = 9 (equation 1)

Squaring the both sides

a^2 + b^2 = 81 - 2ab

a^2 + b^2 = 81 - 36

a^2 + b^2 = 45

Subtracting 2ab from both sides

a^ 2 + b^2 -2ab = 45 - 2ab

( a - b )^2 = 45 - 36

( a - b )^2 = 9

a - b = 3 (equation 2 )

Adding equation 1 with equation 2

2a = 12

a = 6

Putting the value of a in equation 1

b = 9 - 6

b = 3

a = 6 , b = 3

And the other simpler way to solve this questions is -

Write the prime factors of 18.

18 = 1, 2, 3, 6, 9, 18

Now see, putting which 2 prime factors of 18, it satisfies the given equation.

We get 6 and 3

a + b = 9 => 6 + 3 =9

ab = 18 => 6 × 3 = 18