If a/b : c/d, then prove that (a+b) : (c + d) =whole root a^2 +b^2 :whole root c^2 + d^2.
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Step-by-step explanation:
a c
__ = __
b d
adding 1 to both sides
a+b c+d
___ = ____
b d
a+b b
___ = __ ---------A
c+d d
a c
__ = __
b d
square on both sides
a^2 c^2
___ = ____
b^2 d^2
adding 1 both sides
a^2+b^2 c^2+d^2
_______ = _______
b^2 d^2
b^2 a^2 + b^2
___ = ________
d^2 c^2 + d^2
taking square root on both sides
b sqrt(a^2+b^2)
__ = ___________ ---------B
d sqrt(c^2+d^2)
substitute b/d from equation A in B
a+b sqrt(a^2+b^2)
___ = ____________
c+d sqrt(c^2+d^2)
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