What is the value of x?
2 answers:
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Let x be a <span>positive number
</span>![x^2+(x+2)^2=130 \ \ \ \ \ \ [x\ \textgreater \ 0] \\ x^2+x^2+4x+4-130=0 \\ 2x^2+4x-126=0 \\ x^2+2x-63=0 \\ D=b^2-4ac=2^2-4*1*(-63)=4+252=256 \\ x_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{-2б \sqrt{256} }{2*1}= \frac{-2б16 }{2}\\x_1=-9 \ \ \ \ \O\\x_2=7](https://tex.z-dn.net/?f=x%5E2%2B%28x%2B2%29%5E2%3D130%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20%5Bx%5C%20%5Ctextgreater%20%5C%200%5D%20%5C%5C%20x%5E2%2Bx%5E2%2B4x%2B4-130%3D0%20%5C%5C%202x%5E2%2B4x-126%3D0%20%5C%5C%20x%5E2%2B2x-63%3D0%20%5C%5C%20D%3Db%5E2-4ac%3D2%5E2-4%2A1%2A%28-63%29%3D4%2B252%3D256%20%5C%5C%20x_%7B1%2C2%7D%3D%20%5Cfrac%7B-b%D0%B1%20%5Csqrt%7BD%7D%20%7D%7B2a%7D%3D%20%5Cfrac%7B-2%D0%B1%20%20%5Csqrt%7B256%7D%20%20%7D%7B2%2A1%7D%3D%20%20%5Cfrac%7B-2%D0%B116%20%7D%7B2%7D%5C%5Cx_1%3D-9%20%5C%20%5C%20%5C%20%5C%20%5CO%5C%5Cx_2%3D7)
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Answer: the </span><span>number</span> is 7.
Check:
7² + (7+2)² = 49 + 9² = 49 + 81 = 130
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<span>
Answer: the </span><span>number</span> is 7.
Check:
7² + (7+2)² = 49 + 9² = 49 + 81 = 130