Given that (m+n)2=81 and mn=20, what is the value of m2+n2?
Question
Given that (m+n)2=81 and mn=20, what is the value of m2+n2?
Solution
Sure, let's solve this step by step:
Step 1: We know that (m+n)² = m² + 2mn + n². This is given as 81.
Step 2: We also know that mn = 20.
Step 3: We need to find the value of m² + n².
Step 4: We can rearrange the equation from Step 1 to find m² + n² = (m+n)² - 2mn.
Step 5: Substituting the given values into the equation from Step 4, we get m² + n² = 81 - 2*20.
Step 6: Simplifying the right side of the equation gives us m² + n² = 81 - 40 = 41.
So, the value of m² + n² is 41.
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