Question

Cmr :  ( a^2 + b^2 ).( x^2 + y^2 ) = ( ax - by )^2 + ( ay + bx )^2

Answer 1

Ta có:

(\(a^2+b^2\)).(.\(x^2+y^2\)) = \(a^2.\left(x^2+y^2\right)+b^2.\left(x^2+y^2\right)\)

<=>\(ax^2-ay^2+bx^2-by^2\)

<=>  \(\left(ax-by\right)^2+\left(ay+bx\right)^2\)

=> ĐPCM

 

Answer 2

VT: ( ax - by) ^ 2+ (ay +bx)^ 2

= (ax)^2 - 2axby + (by)^2  +   (ay)^2+ 2aybx + (bx)^2

= (ax)^2 + (by)^2 + (ay)^2+ (bx)^2

= a^2 ( x^2 + y^2) + b^2 (x^2 + y^2)

= (a^2 +b^2) ( x^2+ b^2)  = VP   (dpcm)