(5a-2)²-(3a+1)²-a²=60
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Hola.
(5a - 2)² - (3a + 1)² - a² = 60
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(25a² - 20a + 4) - (9a² + 6a + 1) - a² = 60
25a² - 20a + 4 - 9a² - 6a - 1 - a² = 60
25a² - 9a² - a² - 6a - 20a + 4 - 1 = 60
25a² - 10a² - 26a + 4 - 1 = 60
15a² - 26a + 3 = 60
15a² - 26a + 3 - 60 = 0
15a² - 26a - 57 = 0
Resolviendo como una ecuación de segundo grado.
ax² + bx + c = 0
a = 15, b = -26, c = -57
![\mathsf{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}\\\\\\ \mathsf{x=\dfrac{-(-26)\pm\sqrt{(-26)^2-4(15)(-57)}}{2(15)}}\\\\\\ \mathsf{x=\dfrac{+26\pm\sqrt{676-4(-855)}}{30}}\\\\\\ \mathsf{x=\dfrac{26\pm\sqrt{676+3.420}}{30}}\\\\\\ \mathsf{x=\dfrac{26\pm\sqrt{4.096}}{30}}\\\\\\ \mathsf{x=\dfrac{26\pm64}{30}}\\\\\\\\ \mathsf{x'=\dfrac{26+64}{30}}\\\\\\ \mathsf{x'=\dfrac{90}{30}=3}\\\\\\\\ \mathsf{x''=\dfrac{26-64}{30}}\\\\\\ \mathsf{x''=\dfrac{-38}{30}=-1,2\overline{666}} \mathsf{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}\\\\\\ \mathsf{x=\dfrac{-(-26)\pm\sqrt{(-26)^2-4(15)(-57)}}{2(15)}}\\\\\\ \mathsf{x=\dfrac{+26\pm\sqrt{676-4(-855)}}{30}}\\\\\\ \mathsf{x=\dfrac{26\pm\sqrt{676+3.420}}{30}}\\\\\\ \mathsf{x=\dfrac{26\pm\sqrt{4.096}}{30}}\\\\\\ \mathsf{x=\dfrac{26\pm64}{30}}\\\\\\\\ \mathsf{x'=\dfrac{26+64}{30}}\\\\\\ \mathsf{x'=\dfrac{90}{30}=3}\\\\\\\\ \mathsf{x''=\dfrac{26-64}{30}}\\\\\\ \mathsf{x''=\dfrac{-38}{30}=-1,2\overline{666}}](https://tex.z-dn.net/?f=%5Cmathsf%7Bx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%3D%5Cdfrac%7B-%28-26%29%5Cpm%5Csqrt%7B%28-26%29%5E2-4%2815%29%28-57%29%7D%7D%7B2%2815%29%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%3D%5Cdfrac%7B%2B26%5Cpm%5Csqrt%7B676-4%28-855%29%7D%7D%7B30%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%3D%5Cdfrac%7B26%5Cpm%5Csqrt%7B676%2B3.420%7D%7D%7B30%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%3D%5Cdfrac%7B26%5Cpm%5Csqrt%7B4.096%7D%7D%7B30%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%3D%5Cdfrac%7B26%5Cpm64%7D%7B30%7D%7D%5C%5C%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%27%3D%5Cdfrac%7B26%2B64%7D%7B30%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%27%3D%5Cdfrac%7B90%7D%7B30%7D%3D3%7D%5C%5C%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%27%27%3D%5Cdfrac%7B26-64%7D%7B30%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bx%27%27%3D%5Cdfrac%7B-38%7D%7B30%7D%3D-1%2C2%5Coverline%7B666%7D%7D)
![\mathsf{S=\left\{x\in\mathbb{R}~|~\left(\dfrac{-38}{30},~30\right)\right\}} \mathsf{S=\left\{x\in\mathbb{R}~|~\left(\dfrac{-38}{30},~30\right)\right\}}](https://tex.z-dn.net/?f=%5Cmathsf%7BS%3D%5Cleft%5C%7Bx%5Cin%5Cmathbb%7BR%7D%7E%7C%7E%5Cleft%28%5Cdfrac%7B-38%7D%7B30%7D%2C%7E30%5Cright%29%5Cright%5C%7D%7D)
Buenos estudios.
(5a - 2)² - (3a + 1)² - a² = 60
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(25a² - 20a + 4) - (9a² + 6a + 1) - a² = 60
25a² - 20a + 4 - 9a² - 6a - 1 - a² = 60
25a² - 9a² - a² - 6a - 20a + 4 - 1 = 60
25a² - 10a² - 26a + 4 - 1 = 60
15a² - 26a + 3 = 60
15a² - 26a + 3 - 60 = 0
15a² - 26a - 57 = 0
Resolviendo como una ecuación de segundo grado.
ax² + bx + c = 0
a = 15, b = -26, c = -57
Buenos estudios.
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