Question

已知a-b=3,b-c=2,求a∧2-bc+b∧2-ac+c∧2-ab的值

Answer 1

解： ∵ a - b = 3,b - c = 2
∴a - b + b - c = a - c = 5
∴a² - bc + b² - ac + c² - ab
=1/2(a² - 2ab + b² + a² - 2ac + c² + b² - 2bc + c² )
=1/2[(a - b)² + (a - c)² + (b - c)² ]
=1/2(9 + 25 + 4)
=1/2*38
=19

Answer 2

∵a-b=3,b-c=2∴a-c=5
a²-bc+b²-ac+c²-ab
=[(a-b)²+(b-c)²＋(a-c)²]÷2
=(3²+2²+5²)÷2
=19

Answer 3

a-b=3,b-c=2∴a-c=5
a2-bc+b2-ac+c2-ab
=[(a-b)2+(b-c)2＋(a-c)2]÷2
=(32+22+52)÷2
=19

Answer 4

解： ∵ a - b = 3,b - c = 2
∴a - b + b - c = a - c = 5
∴a² - bc + b² - ac + c² - ab
=1/2(a² - 2ab + b² + a² - 2ac + c² + b² - 2bc + c² )
=1/2[(a - b)² + (a - c)² + (b - c)² ]
=1/2(9 + 25 + 4)
=1/2*38
=19