If x + y + z = 11 and xy + yz + zx = 42, then the value of x2 + y2 + z2 is:

Explanation

We are given: x + y + z = 11 xy + yz + zx = 42 We need to find the value of x2 + y2 + z2. Step 1: Use the identity for the sum of squares We know that: x2 + y2 + z2 = (x + y + z)2 - 2(xy + yz + zx) Step 2: Substitute the known values Substitute x + y + z = 11 and xy + yz + zx = 42 into the equation: x2 + y2 + z2 = (11)2 - 2(42) Step 3: Simplify the expression Calculate (11)2 and 2(42): (11)2 = 121 2(42) = 84 Now, substitute these values back: x2 + y2 + z2 = 121 - 84 = 37 Answer: The value of x2 + y2 + z2 is 37.