यदि तीन क्रमागत प्राकृत संख्याओं के वर्गों का योग 110 है तो उनमें से सबसे छोटी प्राकृत संख्या क्‍या है?

Options

A. 8
B. 6
C. 7
D. 5

Answer

D

Explanation

Let the three consecutive numbers are `x,x+1,x+2`.
According to the question
`impliesx^(2)+(x+1)^(2)+(x+2)^(2)=110`
`impliesx^(2)+x^(2)+1+2x+x^(2)+4+4x=110`
`implies 3x^(2)+6x+5=110`
`implies 3x^(2)+6x-35=0`
`implies x^(2)+8x-5x-35=0`
`impliesx^(2)+7x-5x-35=0`
`implies x(x+7)-5(x+7)=0`
`implies (x+7)(x-5)=0`
`implies x=5` & `-7`
`( :. (-)` value cannot considered )
`:. ` Smallest number is `=5`
Alternatively:
You can also solve using options.