# Ram is elder than shyam by 5 years the product of their ages is 66. represent this information by using variable x.

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by afree

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by afree

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=> Shyam is x-5 years old .

x(x-5) = 66

Solving by finding roots

x^2 - 5x - 66 = 0 ]

=> x^2 - 11x + 6x - 66 = 0

=> ( x - 11 ) ( x + 5 ) = 0

=> x = 11 or -5 , but age cant be negative so x is 11 .

So Ram is 11 and Shyam is 6 years old .

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Solving by intuition

x(x-5) = 66

=> x(x-5) = 11 * 6 or (-11 ) * (-6 ) but age cant be -ve . so ( -11 & -6 cant be factors here )

Now x(x-5) = 11 * 6

If x = 11 , x - 5 = 6 true .

If x= 6 , x - 5 = 11 false

so x = 11 is the solution .