SOLUTION: {{{ x^(1/2)-(x-5)^(1/2)=2 }}} I've tried every thing I know and I still don't get a real answer. Would you please help me solve it?

Algebra ->  Radicals -> SOLUTION: {{{ x^(1/2)-(x-5)^(1/2)=2 }}} I've tried every thing I know and I still don't get a real answer. Would you please help me solve it?      Log On


   

Question 265386: +x%5E%281%2F2%29-%28x-5%29%5E%281%2F2%29=2+ I've tried every thing I know and I still don't get a real answer. Would you please help me solve it?
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E%281%2F2%29-%28x-5%29%5E%281%2F2%29=2+ I've tried every thing I know and I still don't get a real answer. Would you please help me solve it?
sorry, accidentally hit post button before trying to solve it, sorry for inconvenience this may of caused
+x%5E%281%2F2%29-%28x-5%29%5E%281%2F2%29=2+
(squared both sides)

+x+%2B+x+-+5+-+2+%2A+%28%28x-5%29%5E%281%2F2%29+%2A+x%5E%281%2F2%29%29+=+4+ (rearranged)
+2%2Ax+-+2+%2A+%28%28x-5%29%5E%281%2F2%29+%2A+x%5E%281%2F2%29%29+=+9+
+-+2+%2A+%28%28x-5%29%5E%281%2F2%29+%2A+x%5E%281%2F2%29%29+=+9+-+2%2Ax+
+4+%2A+%28%28x-5%29+%2A+x%29+=+%289+-+2%2Ax%29%289+-+2%2Ax%29+ (squared both sides)
+4+%2A+%28x%5E2+-+5%2Ax%29+=+81+-+36%2Ax+%2B+4%2Ax%5E2+
+4%2Ax%5E2+-+20%2Ax+=+81+-+36%2Ax+%2B+4%2Ax%5E2+
+4%2Ax%5E2+-+4%2Ax%5E2+-+20%2Ax+%2B+36%2Ax+=+81+ (rearranged)
+16%2Ax+=+81+
+x+=+81%2F16+
check:
+%2881%2F16%29%5E%281%2F2%29+-+%2881%2F16+-+80%2F16%29%5E%281%2F2%29+=+2+ (5*16=80)
+9%2F4+-+%281%2F16%29%5E%281%2F2%29+=+2+
+9%2F4+-+1%2F4+=+2+
+8%2F4+=+2+