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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?
If a + b = 10 and ab = 21, what is the value of a^2 + b^2?
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Practice Questions
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Q1
If a + b = 10 and ab = 21, what is the value of a^2 + b^2?
49
59
61
41
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Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we get a^2 + b^2 = 10^2 - 2*21 = 100 - 42 = 58.
Questions & Step-by-step Solutions
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Q
Q: If a + b = 10 and ab = 21, what is the value of a^2 + b^2?
Solution:
Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we get a^2 + b^2 = 10^2 - 2*21 = 100 - 42 = 58.
Steps: 9
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Step 1: Identify the given equations: a + b = 10 and ab = 21.
Step 2: Recall the identity for a^2 + b^2: a^2 + b^2 = (a + b)^2 - 2ab.
Step 3: Substitute the value of a + b into the identity: (a + b)^2 = 10^2.
Step 4: Calculate 10^2: 10^2 = 100.
Step 5: Substitute the value of ab into the identity: 2ab = 2 * 21.
Step 6: Calculate 2 * 21: 2 * 21 = 42.
Step 7: Now substitute these values into the identity: a^2 + b^2 = 100 - 42.
Step 8: Calculate 100 - 42: 100 - 42 = 58.
Step 9: Therefore, the value of a^2 + b^2 is 58.
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