A) 26
B) 13
C) 21
D) 31
Correct Answer: D
Solution :
Let the two numbers are p and q \[(p>q)\] \[p-q=5\] .....(i) \[{{p}^{2}}+{{q}^{2}}=493\] ?..(ii) Squaring eqn. (i) both sides \[{{(p-q)}^{2}}={{(5)}^{2}}\] \[{{p}^{2}}+{{q}^{2}}-2pq=25\,\,\,\Rightarrow \,\,\,493-2pq=25\] \[-2pq=25-493=-468\] \[2pq=468\Rightarrow \,{{(p+q)}^{2}}={{p}^{2}}+{{q}^{2}}+2pq\] \[=\,\,\,\,493+468=961\] \[p+q=\sqrt{961}=\underline{\mathbf{31}}\]You need to login to perform this action.
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