Question

the ages of three family children can be expressed as consecutive integers . The square of the age of the youngest child is four more than eight times tha age of the oldest child. find the ages of the three childrens. Show your solution​

Answer 1

Answer:

Let the ages be x, x + 1, x + 2.

According to statement

${x}^{2} = 8(x + 2) + 4 \\ {x}^{2} = 8x + 16 + 4 \\ {x}^{2} - 8x - 20 = 0 \\ {x}^{2} - 10x + 2x - 20 = 0 \\ x(x - 10) + 2(x - 10) = 0 \\ (x - 10)(x + 2) = 0 \\ so \: x \: = 10$

so ages are 10, 11, 12 years