यदि `a+b=1, c+d=1` और `a-b=d/c` है तो `c^(2)-d^(2)` का मान क्या होगा?

Options

A. `a/b`
B. `b/a`
C. `1`
D. `-1`

Answer

B

Explanation

`a+b=1`
`c+d=1`
`a-b=d/c`
or `1/(a-b)=c/d`
`(a+b)/(a-b)=c/d( :. a+=1)`
by C & D rule
`implies ((a+b)-(a-b))/((a+b)-(a-b))=(c+d)/(c-d)`
`implies (2a)/(2b)=(c+d)/(c-d)`
`implies a/b=(c+d)/(c-d)`
Now multiply & divide by `(c+d)`
`a/b=((c+d))/((c-d))xx((c+d))/((c+d))=((c+d))/(c^(2)-d^(2))`
`implies a/b=((c+d)^(2))/((c^(2)-d^(2)))`
`c+d=1`
`a/b=1/(c^(2)-d^(2))`
`c^(2)-d^(2)=b/a`