Question:
If \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
If \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
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Use algebraic identities like \( x^4 + y^4 = (x^2 + y^2)^2 - 2x^2y^2 \) when both \(x^2 + y^2\) and \(xy\) are known.
Updated On: Mar 18, 2026
- \(289\)
- \(193\)
- \(337\)
- \(241\)
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The Correct Option is C
Solution and Explanation
Step 1: Use identity to relate \(x^4 + y^4\) with \(x^2 + y^2\) and \(xy\). We start with the identity: \[ x^4 + y^4 = (x^2 + y^2)^2 - 2x^2y^2 \] Step 2: Use the given: \[ x^2 + y^2 = 25, \quad xy = 12 \Rightarrow x^2y^2 = (xy)^2 = 144 \] Step 3: Substitute in the identity: \[ x^4 + y^4 = (25)^2 - 2(144) = 625 - 288 = 337 \].
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