已知a-b=2+根号3,b-c=2-根号3,求a方+b方+c方-ab-bc-ac的值
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已知a-b=2+根号3,b-c=2-根号3,求a方+b方+c方-ab-bc-ac的值
已知a-b=2+根号3,b-c=2-根号3,求a方+b方+c方-ab-bc-ac的值
已知a-b=2+根号3,b-c=2-根号3,求a方+b方+c方-ab-bc-ac的值
由a-b=2+根号3,① b-c=2+根号3,②
①+②,得,a-c=4 ③
a²+b²+c²-ab-bc-ac
=(1/2a²-ab+1/2b²)+(1/2b²-bc+1/2c²)+(1/2a²-ac+1/2c²)
=1/2(a-b)²+1/2(b-c)²+1/2(a-c)²
=1/2[(a-b)²+(b-c)²+(a-c)²]
将①,②,③代入上式,得
.a²+b²+c²-ab-bc-ac
=1/2[(a-b)²+(b-c)²+(a-c)²]
=1/2[(2+根号3)²+(2-根号3)²+4²]
=(1/2)×30=15
不会吗?
由a-b=2+根号3,① b-c=2+根号3,②
①+②,得,a-c=4 ③
a²+b²+c²-ab-bc-ac
=(1/2a²-ab+1/2b²)+(1/2b²-bc+1/2c²)+(1/2a²-ac+1/2c²)
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不会吗?
由a-b=2+根号3,① b-c=2+根号3,②
①+②,得,a-c=4 ③
a²+b²+c²-ab-bc-ac
=(1/2a²-ab+1/2b²)+(1/2b²-bc+1/2c²)+(1/2a²-ac+1/2c²)
=1/2(a-b)²+1/2(b-c)²+1/2(a-c)²
=1/2[(a-b)²+(b-c)²+(a-c)²]
将①,②,③代入上式,得
.a²+b²+c²-ab-bc-ac
=1/2[(a-b)²+(b-c)²+(a-c)²]
=1/2[(2+根号3)²+(2-根号3)²+4²]
=(1/2)×30=15
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