a,b,x,y∈R,且a^2+b^2=1,x^2+y^2=1,证明lax+byl≤1

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a,b,x,y∈R,且a^2+b^2=1,x^2+y^2=1,证明lax+byl≤1a,b,x,y∈R,且a^2+b^2=1,x^2+y^2=1,证明lax+byl≤1a,b,x,y∈R,且a^2+b

a,b,x,y∈R,且a^2+b^2=1,x^2+y^2=1,证明lax+byl≤1
a,b,x,y∈R,且a^2+b^2=1,x^2+y^2=1,证明lax+byl≤1

a,b,x,y∈R,且a^2+b^2=1,x^2+y^2=1,证明lax+byl≤1
(a^2+b^2)(x^2+y^2)=1
a^2x^2+a^2y^2+b^2x^2+b^2y^2=1
(ax+by)^2
=a^2x^2+b^2y^2+2abxy
=1-(a^2y^2+b^2x^2)+2abxy
=1-(ay-bx)^2 ≤ 1
∴| ax+by |≤1