Question

Решите уравнение: √x+1-√9-x = √2x-12

Answer 1

$sqrt{x+1}-sqrt{9-x}=sqrt{2x-12}\\(x+1)-2sqrt{(x+1)(9-x)} +(9-x)=2x-12\\-2, sqrt{(x+1)(9-x)}=2x-22\\sqrt{(x+1)(9-x)}=11-x\\9x-x^2+9-x=121-22x+x^2\\2x^2-30x+112=0\\x^2-15x+56=0; ; to ; ; ; x_1=7; ,; ; x_2=8; ; (teorema; Vieta)\\Proverka:\\x=7:; ; sqrt8-sqrt2=sqrt2; ,; ; 2sqrt2-sqrt2=sqrt2; ,; ; sqrt2=sqrt2; ; verno\\x=8:; ; sqrt9-sqrt1=sqrt4; ,; ; 3-1=2; ,; ; 2=2; ; verno\\Otvet:; ; x=7; ,; x=8; .$

P.S.

Можно было написать ОДЗ.

$ODZ:; left{begin{array}{ccc}x+1geq 0\9-xgeq 0\2x-12geq 0end{array}right; ; left{begin{array}{ccc}xgeq -1\xleq 9\xgeq 6end{array}right; ; left{begin{array}{cc}xleq 9\xgeq 6end{array}right; ; ; Rightarrow ; ; 6leq xleq 9$

Answer 2

Смотри.....................

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