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Hoochie [10]
3 years ago
14

A mother has two children whose ages differ by 5 years. The sum of the squares of their ages is 97. The square of the​ mother's

age can be found by writing the squares of the​ children's ages one after the other as a​ four-digit number. How old is the​ mother?
Mathematics
1 answer:
svetoff [14.1K]3 years ago
4 0

Answer:

41 years old.

Step-by-step explanation:

Let x represent age of younger child.

We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be x+5.

The sum of the squares of their ages is 97. We can represent this information in an equation as:

x^2+(x+5)^2=97

Let us solve for x.

x^2+x^2+10x+25=97

2x^2+10x+25-97=0

2x^2+10x-72=0

Divide both sides by 2:

x^2+5x-36=0

x^2+9x-4x-36=0

x(x+9)-4(x+9)=0

(x+9)(x-4)=0

(x+9)=0 ; (x-4)=0

x=-9 ; x=4

Since age cannot be negative, therefore, age of younger child is 4 years.

Age of older child would be x+5\Rightarrow4+5=9

Therefore, the age of older child would be 9 years.

We have been given that the square of the​ mother's age can be found by writing the squares of the​ children's ages one after the other as a​ four-digit number.

Square of 4: 4^2=16

Square of 9: 9^2=81.

Square of mother's age: 1681

To find mother's age, we need to take positive square root of 1681 as:

\sqrt{1681}=41

Therefore, the mother is 41 years old.

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