Question

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

Answer 1

Step-by-step explanation:

ANSWER:-

Let the age of son be x

Then the age of father be x².

ACCORDING TO QUESTION,

Sum of the age of father is 5 times the age of son when summed up is 66 years.

So that means,

5(x) + x² = 66

x² + 5x - 66 = 0

Now factorising this,

x² + 11x - 6x - 66 = 0

x( x+11) -6( x +11)

= (x-6)(x + 11)

Now we know that x = 6 , - 11

Age can never be in negative.

So the age of Son is 6 years.

And now the age of father is square ie 6×6 = 36 years.

NOTE:-

• X is taken as an constant so that we can make Equations easier
• We used MIDDLE TERM FACTORISATION to factorise x² + 5x - 66
• Factors suitable for 66 to break middle term were 11 and -6 ( 11 × (-6)=66)

Answer 2

Question: The age of father is equal to the square of the age of his son.The sum of the age of father is five times the age of the son is 66 years. Find their ages

Solution: Son's age = 6 years, Father's age =  36 years.

Step by step explanation:

Let the age of the son be $x$ and father be $x^{2}$

According to the given information,

$x^{2} +5x=66\\x^{2} +5x-66=0\\(x-6)(x+11)=0$

∴ $x=6 yrs$

Therefore father's age is $x^{2} =36yrs$