if a:b=c:d , prove that a square c+ a c square :b square d + b d square =(a + - Maths - Mathematical Reasoning

Question

if a:b=c:d , prove that a square c+ a c square :b square d + b d
square =(a + c)cube :( b +d)cube

Ashwini Kumar · Accepted Answer

We have,    a:b=c:d⇒ab=cd=klet∴a=bk  and  c=dkNow, a2c+ac2=bk2×dk+bk×dk2=k3b2d+bd2a+c3=bk+dk3=k3b+d3Now,a2c+ac2b2d+bd2=k3b2d+bd2b2d+bd2=k3Anda+c3b+d3=k3b+d3b+d3=k3Hence,a2c+ac2b2d+bd2=a+c3b+d3∴a2c+ac2:b2d+bd2=a+c3:b+d3

if a:b=c:d , prove that a square c+ a c square :b square d + b d square =(a + c)cube :( b +d)cube .