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If the system of equation r^(2)+s^(2)=t ...

If the system of equation `r^(2)+s^(2)=t` and `r+s+t=(k-3)/(2)` has exactly one real solution, then the value of `k` is

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Eliminating `t`, we get
`r+s+r^(2)+s^(2)=(k-3)/(2)`
or `r^(2)+r+s^(2)+s+(3-k)/(2)=0`
Now for one real solution `'r'`
`D=0`
`:. 1-4(s^(2)+s+(3-k)/(2))=0`
`:. 4s^(2)+4s+5-2k=0`
Now for one real solution `'s'`
`D=0`
`:. 16-16(5-2k)=0`
`:. 1=5-2k`
`:. k=2`
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