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Solve-x-1-4-x-3-x-22-10-x-3-7-

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Question Number 21459 by x² – y²@gmail.com last updated on 24/Sep/17
Solve (√(x + 1 − 4(√(x − 3)))) + (√(x + 22 + 10(√(x − 3)))) = 7
Solvex+1−4x−3+x+22+10x−3=7
Answered by Tikufly last updated on 27/Sep/17
Sol: Put x−3=a^2 , then the equation becomes (√(a^2 +4−4a )) + (√(a^2 +25+10a)) = 7 ⇒(√((a−2)^2 )) + (√((a+5)^2 ))= 7 ⇒(a−2)+(a+5)=7 ⇒2a+3=7 ⇒a = 2 ⇒(√(x−3)) =2 ⇒x−3 = 4 ⇒x = 7
Sol:Putx−3=a2,thentheequationbecomesa2+4−4a+a2+25+10a=7⇒(a−2)2+(a+5)2=7⇒(a−2)+(a+5)=7⇒2a+3=7⇒a=2⇒x−3=2⇒x−3=4⇒x=7

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