Question

determineati numarul natural x siind ca (x+1)×(x+2)+(x+2)×(x+3)​

Answer 1

$(x + 1) (x + 2) + (x + 2)(x + 3) = 50 \\ (x + 2)(x + 1 + x + 3) = 50 \\ (x + 2)(2x + 4) = 50 \\ (x + 2) \cdot2(x + 2) = 50 \\ (x + 2) {}^{2} \cdot 2 = 50 \\ (x + 2) {}^{2} = 25 \\ x {}^{2} + 4x + 4 = 25 \\ x {}^{2} + 4x + 4 - 25 = 0 \\ x {}^{2} + 7x - 3x - 21 = 0 \\ x(x + 7) - 3(x + 7) = 0 \\ (x + 7)(x - 3) = 0 \\ \\ \implies x + 7 = 0 \\\implies x - 3 = 0 \\ \\ \implies\boxed{ x _{1} = - 7 } \\ \implies\boxed{ x _{2} = 3}$