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alexandrabalatskaya
@alexandrabalatskaya
June 2023
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Розв‘яжіть рівняння (4х-5)^2-(2х+3)^2=0
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minster12
Ответ:
(4x-5)^2-(2x+3)^2=0
(4x-5)^2=(2x+3)^2
4x^2-20x+5^2=2x^2+6x+3^3
4x^2-20x+25=2x^2+6x+9
4x^2-14x+16=2x^2
4x^2-2x^2=14x+16
2x^2=14x+16
x^2=7x+16
x^2-7x+8=0
x^2+x-8x+8=0
x(x+8)-8(x+1)=0
(x-8)(x+1)=0
x-8=0|+8 или x+1=0|-1
x=8. x=-1
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Answers & Comments
(4x-5)^2-(2x+3)^2=0
(4x-5)^2=(2x+3)^2
4x^2-20x+5^2=2x^2+6x+3^3
4x^2-20x+25=2x^2+6x+9
4x^2-14x+16=2x^2
4x^2-2x^2=14x+16
2x^2=14x+16
x^2=7x+16
x^2-7x+8=0
x^2+x-8x+8=0
x(x+8)-8(x+1)=0
(x-8)(x+1)=0
x-8=0|+8 или x+1=0|-1
x=8. x=-1