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ScanSolve AI Tutor · Accepted Answer

Step 1: Write down the given equations. We are given: x² + y² = 10; xy = 3 Step 2: Use the algebraic identity for (x+y)². The identity is: (x+y)² = x² + 2xy + y² Rearrange the terms to group x² + y²: (x+y)² = (x² + y²) + 2xy Step 3: Substitute the given values into the identity. Substitute x² + y² = 10 and xy = 3 into the rearranged identity: (x+y)² = (10) + 2(3) Step 4: Simplify the expression. (x+y)² = 10 + 6; (x+y)² = 16 Step 5: Solve for x+y by taking the square root of both sides. x+y = ±√(16); x+y = ± 4 The value of x+y is ± 4.

Answer

Step-by-step solution

Write down the given equations.

Use the algebraic identity for $(x+y)^2$ .

Substitute the given values into the identity.

Simplify the expression.

Solve for $x+y$ by taking the square root of both sides.

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