若关于x的不等式a≤3/4x^2-3x+4≤b的解集恰好是[a,b],则a+b=
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若关于x的不等式a≤3/4x^2-3x+4≤b的解集恰好是[a,b],则a+b=
若关于x的不等式a≤3/4x^2-3x+4≤b的解集恰好是[a,b],则a+b=
若关于x的不等式a≤3/4x^2-3x+4≤b的解集恰好是[a,b],则a+b=
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由韦达定律可以算,答案是4
a<=3/4x^2-3x+4<=b
4a<=x^2-12x+16<=4b……(1)
因为其解为:a<=x<=b,所以3a^2<=3x^2<=3b^2
-12b<=-12x<=-12a两式相加再加16得:
3a^2-12b+16<=3x^2-12x+16<=3b^2-12a+16
又由上(1)式可得:3a^2-12b+16=4a;3b^2-12a+1...
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a<=3/4x^2-3x+4<=b
4a<=x^2-12x+16<=4b……(1)
因为其解为:a<=x<=b,所以3a^2<=3x^2<=3b^2
-12b<=-12x<=-12a两式相加再加16得:
3a^2-12b+16<=3x^2-12x+16<=3b^2-12a+16
又由上(1)式可得:3a^2-12b+16=4a;3b^2-12a+16=4b
两式相减:
3(a+b)(a-b)+12(a-b)=4(a-b);
所以a+b=-8/3
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