Menu Close

Question-103685




Question Number 103685 by bemath last updated on 16/Jul/20
Answered by bobhans last updated on 16/Jul/20
x−(√((2−x)(3−x))) = (√(4−x)){(√(3−x))+(√(2−x))}  2x^2 −5x+6−2x(√((2−x)(3−x))) =  (4−x)(5−2x)+2(√((3−x)(2−x)))  4x−7 =  x(√((2−x)(3−x)))+(4−x)(√((2−x)(3−x)))  4x−7 = 4(√((2−x)(3−x)))  (4x−7)^2  = 16(6−5x+x^2 )  −56x+49 = 96−80x   24x = 47 ⇒ x = ((47)/(24)) ★
$${x}−\sqrt{\left(\mathrm{2}−{x}\right)\left(\mathrm{3}−{x}\right)}\:=\:\sqrt{\mathrm{4}−{x}}\left\{\sqrt{\mathrm{3}−{x}}+\sqrt{\mathrm{2}−{x}}\right\} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}−\mathrm{2}{x}\sqrt{\left(\mathrm{2}−{x}\right)\left(\mathrm{3}−{x}\right)}\:= \\ $$$$\left(\mathrm{4}−{x}\right)\left(\mathrm{5}−\mathrm{2}{x}\right)+\mathrm{2}\sqrt{\left(\mathrm{3}−{x}\right)\left(\mathrm{2}−{x}\right)} \\ $$$$\mathrm{4}{x}−\mathrm{7}\:= \\ $$$${x}\sqrt{\left(\mathrm{2}−{x}\right)\left(\mathrm{3}−{x}\right)}+\left(\mathrm{4}−{x}\right)\sqrt{\left(\mathrm{2}−{x}\right)\left(\mathrm{3}−{x}\right)} \\ $$$$\mathrm{4}{x}−\mathrm{7}\:=\:\mathrm{4}\sqrt{\left(\mathrm{2}−{x}\right)\left(\mathrm{3}−{x}\right)} \\ $$$$\left(\mathrm{4}{x}−\mathrm{7}\right)^{\mathrm{2}} \:=\:\mathrm{16}\left(\mathrm{6}−\mathrm{5}{x}+{x}^{\mathrm{2}} \right) \\ $$$$−\mathrm{56}{x}+\mathrm{49}\:=\:\mathrm{96}−\mathrm{80}{x}\: \\ $$$$\mathrm{24}{x}\:=\:\mathrm{47}\:\Rightarrow\:{x}\:=\:\frac{\mathrm{47}}{\mathrm{24}}\:\bigstar \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *