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The sum of square of two numbers is 85 the difference between the number is 1 find the numbers

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Answer:

Let's assume that the two numbers are x and y, where x is greater than y.

From the given information, we can write two equations:

x^2 + y^2 = 85 (Equation 1)

x - y = 1 (Equation 2)

We can solve Equation 2 for x and substitute into Equation 1:

x = y + 1

(x = y + 1) into (Equation 1)

(y + 1)^2 + y^2 = 85

Simplifying this equation, we get:

2y^2 + 2y - 84 = 0

Dividing both sides by 2, we get:

y^2 + y - 42 = 0

Factoring this equation, we get:

(y + 7)(y - 6) = 0

Therefore, y = -7 or y = 6. Since x is greater than y, we can ignore the negative value.

So, y = 6 and x = y + 1 = 7.

Therefore, the two numbers are 6 and 7.

User Vitalii Chmovzh
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