Toán Lớp 9: Chứng minh : (ac + bd)2 + (ad – bc)2 = (a2 + b2)(c2 + d2)
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Toán Lớp 9: Chứng minh : (ac + bd)2 + (ad – bc)2 = (a2 + b2)(c2 + d2)
Comments ( 1 )
Ta có :
VT=(ac + bd)^2 + (ad – bc)^2
=a^2c^2+2abcd+b^2d^2+a^2d^2-2abcd+b^2c^2
=a^2c^2+b^2d^2+a^2d^2+b^2c^2
=(a^2c^2+a^2d^2)+(b^2d^2+b^2c^2)
=a^2(c^2+d^2)+b^2(c^2+d^2)
=(a^2+b^2)(c^2+d^2)=VP