Question

The difference of the squares of 2 number is 45 the square of smaller number is 4 times longer number. find the number

Answer 1

Answer:

a=9;b=6

Step-by-step explanation:

given a²-b² = 45

if b is taken as the smaller no.

then given b² = 4a

=> a² - 4a = 45

=>  a² - 4a - 45 =0

=> a² - 9a + 5a - 45 = 0

=> a(a-9) - 5(a-9) = 0

=> (a-9)(a-5) = 0

=> a-9 = 0   => a=9  => b= √(4*9) = √36 = 6 => b=6

=> a-5 = 0   => a=5  => b= √(4*5) = √20  (not suitable)