Given that m2+n2=230 and mn=113, find the value of (m−n)2.

Question

Given that m2+n2=230 and mn=113, find the value of (m−n)2.

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Solution

Sure, let's solve this step by step:

The formula for (m−n)² is m² - 2mn + n².

We know that m² + n² = 230 and mn = 113.

Substitute these values into the formula:

(m−n)² = 230 - 2*113 = 230 - 226 = 4.

So, the value of (m−n)² is 4.

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