若(a+b)²=13,(a-b)²=27,求2a²+6ab+2b²的值
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若(a+b)²=13,(a-b)²=27,求2a²+6ab+2b²的值
若(a+b)²=13,(a-b)²=27,求2a²+6ab+2b²的值
若(a+b)²=13,(a-b)²=27,求2a²+6ab+2b²的值
(a+b)^2=a^2+b^2+2ab=13
(a-b)^2=a^2+b^2-2ab=27
2(a^2+b^2)=40
a^2+b^2=20
2ab=-7
2a²+6ab+2b²=40-21=19
∵(a+b)²=13,(a-b)²=27
∴a²+b²+2ab=13
a²+b²-2ab=27
∴a²+b²=(13+27)÷2=20
2ab=(13-27)÷2=-7
2a²+6ab+2b²
=2(a²+b²)+3×2ab
=2×20+3×(-7)
=40-21
=19
(a+b)²=13,(a-b)²=27
即:a²+2ab+b²=13, a²-2ab+b²=27
相加:2(a²+b²)=40
相减:4ab=-14 2ab=-7
2a²+6ab+2b²=40-21=19
(a+b)²=13,a²+2ab+b²=13;
(a-b)²=27,a²-2ab+b²=27;
两式相加:2a²+2b²=40;
两式相减:4ab=-14,6ab=-21;
2a²+6ab+2b²=40-21=19
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