| Directions: In each of the following questions two equations are given. You have to solve both the equations and find out values of x, y and give answer. [NICL (AO) 2014] |
| I. \[{{x}^{2}}-{{(16)}^{2}}={{(23)}^{2}}-56\] |
| II. \[{{y}^{1/3}}-55+376={{(18)}^{2}}\] |
A) If \[x>y\]
B) If \[x\le y\]
C) If \[x<y\]
D) If \[x\ge y\]
E) If relationship between x and y cannot be determined
Correct Answer: B
Solution :
| I. \[{{x}^{2}}-{{(16)}^{2}}={{(23)}^{2}}-56\] |
| \[\Rightarrow \] \[{{x}^{2}}-256=529-56\Rightarrow {{x}^{2}}=729\] |
| \[\therefore \] \[x=\pm \,27\] |
| II. \[{{y}^{1/3}}-55+376={{(18)}^{2}}\] |
| \[\Rightarrow \] \[{{y}^{1/3}}-55+376=324\,\,\Rightarrow \,\,{{y}^{1/3}}=3\] |
| \[\Rightarrow \] \[y=27\] [taking cube on both sides] |
| \[\therefore \] \[x\le y\] |
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