已知a⊕b表示(a+b)×(a-b),试计算:(6⊕4)⊕(5⊕3).

问题描述:

已知a⊕b表示(a+b)×(a-b),试计算:(6⊕4)⊕(5⊕3).

(6⊕4)⊕(5⊕3)
=(6^2-4^2)^2-(5^2-3^2)^2
=20^2-16^2
=144

a⊕b表示(a+b)×(a-b)
即a⊕b表示a²-b²
(6⊕4)⊕(5⊕3)
=(6²-4²)²-(5²-3²)²
=20²-16²
=144

(6⊕4)
=(6+4)(6-4)
=20
(5⊕3)
=(5+3)(5-3)
=16
20⊕16
=(20+16)(20-16)
=36×4
=144

(6⊕4)⊕(5⊕3)
=【(6+4)(6-4)】⊕【(5+3)(5-3)】
=20⊕16
=(20+16)(20-16)
=36×4
=144

(6⊕4)=(6+4)(6-4)=20
(5⊕3)=(5+3)(5-3)=16
20⊕16=(20+16)(20-16)=144
所以原式=144

(6⊕4)⊕(5⊕3)
=[(6+4)(6-4)]⊕[(5+3)(5-3)]
=20⊕16
=(20+16)(20-16)
=36*4
=144