SOLUTION: x= sqrt(3+2sqrt2) + sqrt(3-2sqrt2) a) Find the exact value of x^2 without using a calculator b) Hence, determine the value of x.

Algebra ->  Linear-equations -> SOLUTION: x= sqrt(3+2sqrt2) + sqrt(3-2sqrt2) a) Find the exact value of x^2 without using a calculator b) Hence, determine the value of x.      Log On


   

Question 1128590: x= sqrt(3+2sqrt2) + sqrt(3-2sqrt2)
a) Find the exact value of x^2 without using a calculator
b) Hence, determine the value of x.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
x^2 = 3+%2B+2%2Asqrt%282%29 + 3-2%2Asqrt%282%29 + 2%2Asqrt%283+%2B+2%2Asqrt%282%29%29%2Asqrt%283+-+2%2Asqrt%282%29%29 = 6+%2B+2%2Asqrt%28%283+%2B+2%2Asqrt%282%29%29%2A%283+-+2%2Asqrt%282%29%29%29 = 


= 6+%2B+2%2Asqrt%28%283%5E2+-+%282%2Asqrt%282%29%29%5E2%29%29 = 6+%2B+2%2Asqrt%289-4%2A2%29 = 6+%2B+2%2Asqrt%281%29 = 6 + 2 = 8.