Solve for x : 9x^2 - 9(a+b)x + (2a^2+5ab + 2b^2) =0

Asked by Fathima | 31st Mar, 2017, 05:35: PM

Expert Answer:

begin mathsize 16px style Consider comma space 9 straight x squared minus 9 left parenthesis straight a plus straight b right parenthesis straight x plus left parenthesis 2 straight a squared plus 5 ab plus 2 straight b squared right parenthesis equals 0 space
rightwards double arrow 9 straight x squared space minus space 9 left parenthesis straight a space plus space straight b right parenthesis straight x space plus space left parenthesis 2 straight a squared space plus space 4 ab space plus space ab space plus space 2 straight b squared right parenthesis space equals space 0 space
rightwards double arrow 9 straight x squared space minus space 9 left parenthesis straight a space plus space straight b right parenthesis straight x space plus space left square bracket 2 straight a left parenthesis straight a space plus space 2 straight b right parenthesis space plus space straight b left parenthesis straight a space plus space 2 straight b right parenthesis right square bracket space equals space 0 space
rightwards double arrow 9 straight x squared space minus space 9 left parenthesis straight a space plus space straight b right parenthesis straight x space plus space left square bracket left parenthesis straight a space plus space 2 straight b right parenthesis left parenthesis 2 straight a space plus space straight b right parenthesis right square bracket space equals space 0
rightwards double arrow 9 straight x squared space – space 3 left square bracket left parenthesis straight a space plus space 2 straight b right parenthesis space plus space left parenthesis 2 straight a space plus space straight b right parenthesis right square bracket straight x space plus space left square bracket left parenthesis straight a space plus space 2 straight b right parenthesis left parenthesis 2 straight a space plus space straight b right parenthesis right square bracket space equals space 0 space
rightwards double arrow 9 straight x squared space – space 3 left parenthesis straight a space plus space 2 straight b right parenthesis straight x space minus space 3 left parenthesis 2 straight a space plus space straight b right parenthesis straight x space plus space left square bracket left parenthesis straight a space plus space 2 straight b right parenthesis left parenthesis 2 straight a space plus space straight b right parenthesis right square bracket space equals space 0 space
rightwards double arrow 3 straight x left square bracket 3 straight x space space – space left parenthesis straight a space plus space 2 straight b right parenthesis right square bracket space minus space left parenthesis 2 straight a space plus space straight b right parenthesis left square bracket 3 straight x space plus space left parenthesis straight a space – space 2 straight b right parenthesis right square bracket space equals space 0 space
rightwards double arrow left square bracket 3 straight x space space – space left parenthesis straight a space plus space 2 straight b right parenthesis right square bracket left square bracket 3 straight x space minus space left parenthesis 2 straight a space plus space straight b right parenthesis right square bracket space equals space 0 space
rightwards double arrow left square bracket 3 straight x space – space left parenthesis straight a space plus space 2 straight b right parenthesis right square bracket space equals space 0 space or space left square bracket 3 straight x space minus space left parenthesis 2 straight a space plus space straight b right parenthesis right square bracket space equals space 0 space
rightwards double arrow 3 straight x space space equals space space left parenthesis straight a space plus space 2 straight b right parenthesis space or space 3 straight x space equals space left parenthesis 2 straight a space plus space straight b right parenthesis space
rightwards double arrow straight x space equals space fraction numerator left parenthesis straight a space plus space 2 straight b right parenthesis over denominator 3 end fraction space space or space space straight x equals fraction numerator left parenthesis 2 straight a space plus space straight b right parenthesis over denominator 3 end fraction end style

Answered by Rebecca Fernandes | 31st Mar, 2017, 09:34: PM