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crazy20002
@crazy20002
October 2021
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2407Alexa
√(3х²+5х+8)=(3+х)
(√(3х²+5х+8))²=(3+х)²
3х²+5х+8=9+6х+х²
3х²+5х+8-9-6х-х²=0
2х²-х-1=0
D=(-(-1))²-4×2×(-1)=1+8=9
x1=(-(-1)-√9)/2×2=(1-3)/4=(-2)/4=(-1/2)=-0,5;
x2=(-(-1)+√9)/2×2=(1+3)/4=4/4=1.
Проверки:
√(3×(-0,5)²+5×(-0,5)+8)=3+(-0,5)
√(3×0,25-2,5+8)=2,5
√(0,75-2,5+8)=2,5
√6,25=2,5
2,5=2,5-истина.
√(3×1²+5×1+8)=3+1
√(3+5+8)=4
√16=4
4=4-истина.
Ответ: х1=-0,5 и х2=1.
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Answers & Comments
(√(3х²+5х+8))²=(3+х)²
3х²+5х+8=9+6х+х²
3х²+5х+8-9-6х-х²=0
2х²-х-1=0
D=(-(-1))²-4×2×(-1)=1+8=9
x1=(-(-1)-√9)/2×2=(1-3)/4=(-2)/4=(-1/2)=-0,5;
x2=(-(-1)+√9)/2×2=(1+3)/4=4/4=1.
Проверки:
√(3×(-0,5)²+5×(-0,5)+8)=3+(-0,5)
√(3×0,25-2,5+8)=2,5
√(0,75-2,5+8)=2,5
√6,25=2,5
2,5=2,5-истина.
√(3×1²+5×1+8)=3+1
√(3+5+8)=4
√16=4
4=4-истина.
Ответ: х1=-0,5 и х2=1.