Toán Lớp 9: √x²+2x+1 + √x²-2x+1 = 2

Question

Toán Lớp 9:  √x²+2x+1   +   √x²-2x+1     =    2

lanthuhoa · Answer

Giải đáp:    ( left[  begin{array}{l}x= sqrt{ frac{1}{4}}   x=- sqrt{ frac{1}{4}} end{array}  right. )   Lời giải và giải thích chi tiết:   &radic;x&sup2;+2x+1 + &radic;x&sup2;-2x+1 = 2   &hArr; &radic;(x+1)&sup2; + &radic;(x-1)&sup2; = 2    &hArr; |x+1| + |x - 1| = 2    &hArr; (|x + 1| + |x - 1|)&sup2; = 2&sup2;   &hArr; |x + 1|&sup2; + |x - 1|&sup2; + 2|x - 1||x + 1| = 4   &hArr; (x + 1)&sup2; + (x - 1)&sup2; + 2|(x - 1)(x + 1)| = 4   &hArr; x&sup2; + 2x + 1 + x&sup2; - 2x + 1 + 2|x&sup2; - 1| = 4   &hArr; 2x&sup2; + 2 + 2|x&sup2; - 1| = 4   &hArr; 2(x&sup2; + |x&sup2; - 1|) = 2   &hArr; x&sup2; + |x&sup2; - 1| = 2   &hArr; |x&sup2; + 1| = 2 - x&sup2;   &hArr; ( left[  begin{array}{l}x^{2}+1=2-x^{2}   x^{2}+1=x^{2}-2 end{array}  right. )    &hArr; ( left[  begin{array}{l}2x^{2}=1  0=1 end{array}  right. )    &hArr; x&sup2; = $ frac{1}{2}$    &hArr; ( left[  begin{array}{l}x= sqrt{ frac{1}{4}}   x=- sqrt{ frac{1}{4}} end{array}  right. )

truonganhthi · Answer

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