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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x^2+5x=66.......x square plus five x =sixty six
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Let Ram be x years old .
=> 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 .
=> 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 .
_____________________________________________
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 .
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