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If a/b and c/d are rational numbers then what is a×b/b×d |
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Answer»
ANSWER If a=c, then a+ b
=c+ d
⇒ b
= d
⇒b=d So, let a
=c. Then, there exists a positive rational number x such that a=c+x. Now, ⇒a+ b
=c+ d
⇒c+x+ b
=c+ d
[∵a=c+x] ⇒x+ b
= d
⇒(x+ b
) 2 =( d
) 2
⇒x 2 +2 b
x+b=d ⇒ b
= 2x d−x 2 −b
⇒ b
is rational [∴d,x,b are rationals∴ 2x d−x 2 −b2
is rational] ⇒ b is the square of a rational number. From(i), we have d
=x+ b
⇒ d
is rational ⇒ d is the square of a rational number. Hence, EITHER a=c and b=d or b and d are the SQUARES of rationals.
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