1. If  2power x+5 X 3 power 2x-9 =3022 find value of x ?
 
 
2. x= square root of blank end root3+square root of blank end root2divided bysquare root of blank end root3+square root of blank end root2 and y= square root of blank end root3-square root of blank end root2divided bysquare root of blank end root3+square root of blank end root2 find x2 + y2-xy

Asked by vaibhavmishratempleton | 3rd Jul, 2014, 10:06: PM

Expert Answer:

x equals square root of 3 space plus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 space space space space space space comma space y space equals square root of 3 space minus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 x squared plus y squared minus x y space equals space left parenthesis x minus y right parenthesis squared plus x y  left parenthesis x minus y right parenthesis squared space equals space left parenthesis square root of 3 space plus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 space minus square root of 3 space plus space fraction numerator square root of 2 over denominator square root of 3 end fraction minus square root of 2 space right parenthesis squared equals left parenthesis fraction numerator 2 square root of 2 over denominator square root of 3 end fraction right parenthesis squared equals 8 over 3 x y equals left parenthesis square root of 3 space plus fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 right parenthesis space left parenthesis square root of 3 space minus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 right parenthesis space space space space equals left square bracket space left parenthesis square root of 3 space plus square root of 2 right parenthesis squared minus 2 over 3 right square bracket space space space space equals 3 plus space 2 space plus 2 square root of 6 space minus 2 over 3 space space space space equals 13 over 3 plus 2 square root of 6  x squared space plus space y squared minus x y space equals space 8 over 3 plus 13 over 3 plus 2 square root of 6 space space space space space space space space space space space space space space space space space space space space equals space 21 over 3 plus 2 square root of 6 space space space space space space space space space space space space space space space space space space space space equals space 7 space plus 2 square root of 6x equals square root of 3 space plus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 space space space space space space comma space y space equals square root of 3 space minus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 x squared plus y squared minus x y space equals space left parenthesis x minus y right parenthesis squared plus x y  left parenthesis x minus y right parenthesis squared space equals space left parenthesis square root of 3 space plus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 space minus square root of 3 space plus space fraction numerator square root of 2 over denominator square root of 3 end fraction minus square root of 2 space right parenthesis squared equals left parenthesis fraction numerator 2 square root of 2 over denominator square root of 3 end fraction right parenthesis squared equals 8 over 3 x y equals left parenthesis square root of 3 space plus fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 right parenthesis space left parenthesis square root of 3 space minus space fraction numerator square root of 2 over denominator square root of 3 end fraction plus square root of 2 right parenthesis space space space space equals left square bracket space left parenthesis square root of 3 space plus square root of 2 right parenthesis squared minus 2 over 3 right square bracket space space space space equals 3 plus space 2 space plus 2 square root of 6 space minus 2 over 3 space space space space equals 13 over 3 plus 2 square root of 6  x squared space plus space y squared minus x y space equals space 8 over 3 plus 13 over 3 plus 2 square root of 6 space space space space space space space space space space space space space space space space space space space space equals space 21 over 3 plus 2 square root of 6 space space space space space space space space space space space space space space space space space space space space equals space 7 space plus 2 square root of 6

Answered by Vimala Ramamurthy | 4th Jul, 2014, 12:53: PM