Question

the age of father is equal to the square of the age of his son. the sum of the age of father and five times the age of the son is 66 find their ages​

Answer 1

Quadratic Equations

Solution :

Let the age of son be x years.

Then , Father's age = $\mathsf{x} ^{2}$ years.

According to the second condition ,

$\mathsf{{x} ^{2}\:+\:5x \:=\:66}$

$\mathsf{{x} ^{2}\:+\:5x\:-\:66\:=\:0}$

$\mathsf{{x} ^{2}\:+\:11x\:-6x\:-\:66\:=\:0}$

$\mathsf{x(\:x\:+\:11\:)\:-6(\:x\:+\:11\:)\:=\:0}$

$\mathsf{(\:x\:-\:6\:)(\:x\:+\:11\:)\:=\:0}$

$\mathsf{(\:x\:-\:6\:)\:=\:0, \:(\:x\:+\:11\:)\:=\:0}$

$\mathsf{x\:=\:6,-11}$

So, Age cannot be in negative. It must be a positive value of x. i. e. 6.

So, Son's age = x = 6 years.

Father's age = $\mathsf{x} ^{2}$ = $\mathsf{6} ^{2}$ years. = 36 years.

Son's age = $\boxed{\mathsf{6\:years}}$

Father's age = $\boxed{\mathsf{36\:years}}$

Answer 2

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