obs23 wrote:
\((\sqrt{15+4\sqrt{14}}+\sqrt{15-4\sqrt{14}})^2\)
A. 28
B. 29
C. 30
D. 31
E. 32
We can let
x = √(15 + 4√14) and
y = √(15 - 4√14).
Since (x + y)^2 = x^2 + y^2 + 2xy, we have:
x^2 = (15 + 4√14)
y^2 = (15 - 4√14)
and
2xy is
2√(15 + 4√14) x √(15 - 4√14)
2√[(15 + 4√14)(15 - 4√14)]
Since (15 + 4√14)(15 - 4√14) can be written as a difference of squares, we have:
2√[(15^2) - (4√14)^2]
2√[225 - 224] = 2
Thus, the total value is:
(15 + 4√14) + (15 - 4√14) + 2 = 32
Answer: E
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