Find a quadratic equation whose roots `x_(1)` and `x_(2)` satisfy the condition `x_(1)^(2)+x_(2)^(2)=5,3(x_(1)^(5)+x_(2)^(5))=11(x_(1)^(3)+x_(2)^(3))` (assume that `x_(1),x_(2)` are real)

Explanation

To find a quadratic equation whose roots \( x_1 \) and \( x_2 \) satisfy the conditions given, we can follow these steps:

### Step 1: Use the identity for the sum of squares
We know that:
\[ x_1^2 + x_2^2 = (x_1 + x_2)^2 - 2x_1x_2 \]
Let \( s = x_1 + x_2 \) (the sum of the roots) and \( p = x_1 x_2 \) (the product of the roots). Then we can rewrite the first condition:
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