SOLUTION: I. Find the square of √a + √b and -√a-√b. II. Use the result of part I. to find the square roots of 10+√84.

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Question 1016336: I. Find the square of √a + √b and -√a-√b.
II. Use the result of part I. to find the square roots of 10+√84.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%28a%29+%2B+sqrt%28b%29%29%5E2+=+a%2B2sqrt%28ab%29+%2Bb
If we let 10+%2B+sqrt%2884%29+=+a%2B2sqrt%28ab%29+%2Bb we then get
a + b = 10 and ab = 21 by equating coefficients of like terms.
==> b+=+21%2Fa, and so a%2B21%2Fa+=+10, or a%5E2-10a%2B21=0
==> a = 3 or 7, which gives b = 7 or 3, respectively.
Either way, we get sqrt%2810%2Bsqrt%2884%29%29+=+sqrt%283%29+%2Bsqrt%287%29.