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What three consecutive integers have a …

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What three consecutive integers have a sum of 21
  • 2 answers

Sia ? 4 years, 8 months ago

Let the required numbers be (a - d), a, (a + d)
Sum of these numbers = (a - d) + a + (a + d) = 3a
{tex}\therefore{/tex}sum of these squares = (a-d)2+a2+(a+d)2=3a2+2d2

According to the question,we are given that,

Sum of three numbers = 21
{tex}\therefore{/tex}3a = 21
a = 7

Also,sum of the squares of three numbers=165
 {tex}\Rightarrow{/tex}3a2 + 2d2=165

{tex}\Rightarrow{/tex}3(7)2+2d2=165

 {tex}\Rightarrow{/tex}2d2 =18
{tex}\Rightarrow{/tex}d2=9
{tex}\Rightarrow{/tex}d={tex} \pm {/tex}3
Thus, a=7 and d={tex} \pm {/tex}3
Hence, the required numbers are (4, 7, 10) or (10, 7, 4)

Tarush Rai 4 years, 8 months ago

Easy way
http://mycbseguide.com/examin8/

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