Name: Sandy

Level: grade 11

Who is asking the question: teacher

Qustion:

The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers.

Hi Sandy

Suppose that the numbers are x and y with x>y. Your two conditions then are

and

2x - y = 11.

Solve the second condition for y to get y = 2x - 11 and then substitute into the first giving

which, when simplified, is

.
Solving, using the general quadratic, gives x=2 or x=6.8. Since y = 2x - 11 the two numbers are 2 and -7 or 6.8 and 2.6.

Cheers,

Penny.

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