Algebra: Solve x for [ {2 + (3^1/2)}^1/2]^x + [{2 – (3^1/2)}^1/2]^x = 4?
Answer The trick is this. SQUARE THE EQUATION. Note that : [{2 + (3^1/2)}^1/2]^x = [{2 + (3^1/2)}^(x/2)] We get [ {2 + (3^1/2)}^1/2]^x + [{2 – (3^1/2)}^1/2]^x = 4 {2 + (3^1/2)}^x + 2 [{2 + (3^1/2)}^(x/2)]*[{2 – (3^1/2)}^(x/2)] + {2 – (3^1/2)}^x = 16 and [{2 + (3^1/2)}^(x/2)]*[{2 – (3^1/2)}^(x/2)] equals to...
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