若a^2+b^2+2a-b=-5/4,先化简(a-5b)(-a-5b)-(-a+5b)^2,再求值
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若a^2+b^2+2a-b=-5/4,先化简(a-5b)(-a-5b)-(-a+5b)^2,再求值
若a^2+b^2+2a-b=-5/4,先化简(a-5b)(-a-5b)-(-a+5b)^2,再求值
若a^2+b^2+2a-b=-5/4,先化简(a-5b)(-a-5b)-(-a+5b)^2,再求值
已知,a^2+b^2+2a-b = -5/4 ,
整理得:(a+1)^2+(b-1/2)^2 = 0 ,
所以,a+1 = 0 ,b-1/2 = 0 ,
解得:a = -1 ,b = 1/2 .
化简:
原式
= (a-5b)(-a-5b)-(a-5b)^2
= (a-5b)[(-a-5b)-(a-5b)]
= (a-5b)[-2a]
= -2a^2+10ab
将 a = -1 ,b = 1/2 代入,可得:
原式
= -2(-1)^2+10(-1)(1/2)
= -2-5
= -7
(a-5b)(-a-5b)-(-a+5b)^2
=(-a+5b)(a+5b)-(-a+5b)^2
=(-a+5b)(a+5b+a-5b)
=(-a+5b)*2a
剩下来的就自己做吧
a^2 + b^2 + 2a - b =-5/4
a^2 + b^2 + 2a - b + (1 + 1/4)=0
(a^2 + 2a + 1) + (b^2 - b + 1/4)=0
(a+1)^2 + (b - 1/2)^2 =0
∴(a+1)^2=0 , (b - 1/2)^2=0
则:a=-1 , b=1/2
(a-5b)(-a-...
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a^2 + b^2 + 2a - b =-5/4
a^2 + b^2 + 2a - b + (1 + 1/4)=0
(a^2 + 2a + 1) + (b^2 - b + 1/4)=0
(a+1)^2 + (b - 1/2)^2 =0
∴(a+1)^2=0 , (b - 1/2)^2=0
则:a=-1 , b=1/2
(a-5b)(-a-5b)-(-a+5b)^2
=[(-5b)^2 - a^2] - (a^2 - 10ab + 25b^2)
=25b^2 - a^2 - a^2 + 10ab - 25b^2
=-2a^2 + 10ab
=-2*(-1)^2 + 10*(-1)*(1/2)
=-7
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