Question

the sum of squares of two consecutive even number is 340. find the numbers

Answer 1

this is your answer.pls mark brainleist

Answer 2

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☞ Numbers are 12 and 14

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✭ The sum of the squares of the two consecutive even numbers is 340

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◈ The Numbers?

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Let the two numbers be x and x+2

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➝ $\sf{ (x)^2 + (x+2)^2 = 340}$

➝ $\sf{ x^2 + x^2 + 4x + 4= 340\qquad\bigg\lgroup (a^2+b^2) = a^2+2ab+b^2\bigg\rgroup}$

➝ $\sf{ 2x^2 + 4x = 340-4 }$

➝ $\sf{ 2x^2 + 4x - 336 = 0}$

➝ $\sf{x^2 + 2x - 168 = 0 \qquad\bigg\lgroup Taking \ 2 \ commonn\bigg\rgroup}$

➝ $\sf{x^2 +(14-12)x-168 = 0 }$

➝ $\sf{x^2 +14x -12x -168=0}$

➝ $\sf{x(x+14) -12(x+14) = 0}$

➝ $\sf{(x + 14)(x - 12) = 0 }$

➝ $\sf{ x = -14 (Neglected) }$

➝ $\sf{\orange{ x = 12 }}$

≫ First Number = x = 12

≫ Another number = x+2 = 12+2 = 14

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