логарифмы, нужна помощь в решении уравнения! lg(x+√2) = lg(3+2√2)

Kaleso @Kaleso

August 2022 1 8 Report

логарифмы, нужна помощь в решении уравнения!
lg(x+√2) = lg(3+2√2) - lg(√2+1)

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kirichekov

Verified answer

Lg(x+√2)+lg(√2+1)=lg(3+2√2) .ОДЗ: х+√2>0, x>-√2
lg [(x+√2)*(√2+1) ]=lg(3+2√2)
(x+√2)*(√2+1)=3+2√2
√2 *x+2+x+√2=3+2√2
x(√2+1)=3-2-√2+2√2
x(√2+1)=1+√2
x=(√2+1)/(√2+1)
x=1

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