Math, asked by salujiarw, 8 months ago

the sum of squares of two consecutive natural numbers is 244; find the number. complete answer

Answers

Answered by TheVenomGirl
2

AnSwer :

  • The sum of squares of two consecutive natural number is 244, and the numbers are 12 and 10. 

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GiVen :

  • Sum of squares of two consecutive natural number is 244.

To Find :

  • Original number = ?

SoluTion :

  • Let us consider the first number as x, and the second number as x + 2  

According to the question,

\longmapsto \sf \: ({x})^{2}+({x}+2)^{2}= 244 \\  \\ \longmapsto   \sf\: {x}^{2}+{x}^{2}+4 {x}+4= 244 \\  \\ \longmapsto \sf \:  2 x^{2}+4 x=244-4 \\  \\ \longmapsto  \sf\:  2 x^{2}+4 x=240 \\  \\ \longmapsto \sf \:  2 x^{2}+4 x-240=0 \\  \\ \longmapsto \sf \: 2\left({x}^{2}+2 {x}-120\right)=0 \\  \\ \longmapsto \sf \: \left({x}^{2}+2 {x}-120 \right)=0 \\  \\ \longmapsto  \sf\: {x}^{2}+12 {x}-10 {x}-120 \\  \\ \longmapsto  \sf\: {x}({x}+12)-10({x}+12)=0 \\  \\ \longmapsto \sf \: (x-10)(x+12)=0 \\ \\  \longmapsto \:{ \underline{ \boxed{ \bf{ \purple{ \: x=10,-12 \: }}}}} \:  \bigstar

Therefore, as number can't be negative, original number is 10 and +12.

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Answered by Anonymous
2

Solution :-

Let's :-

  • First number = x

  • 2nd number = x + 2

According to Question :

→ ( x )² + ( x + 2 )² = 244

→ x² + x² + 4 + 4x = 244

→ 2x² + 4x + 4 - 244 = 0

→ 2x² + 4x - 240 = 0

Both side divided by 2

→ x² + 2x - 120 = 0

By splitting middle term

→ x² + 12x - 10x - 120 = 0

→ x ( x + 12 ) - 10 ( x + 12 ) = 0

→ ( x - 10 ) ( x + 12 ) = 0

→ x = 10

→ x = - 12

First number = 10

Second number = 10 + 2 = 12

Verification :-

( 10 )² + ( 12 )² = 244

100 + 144 = 244

244 = 244

LHS = RHS

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