Докажите тождество (ax+by)^2+(ay-bx)^2=(a^2+b^2)(x^2+y^2)
(ax+by)^2+(ay-bx)^2=a2x2+2axby+b2y2+a2y2-2aybx+b2x2=(a2x2+a2y2)+(b2y2+b2x2)=a2(x2+y2)+b2(y2+x2)=(a2+b2)(x2+y2)
Тождество доказана
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
(ax+by)^2+(ay-bx)^2=a2x2+2axby+b2y2+a2y2-2aybx+b2x2=(a2x2+a2y2)+(b2y2+b2x2)=a2(x2+y2)+b2(y2+x2)=(a2+b2)(x2+y2)
Тождество доказана