Question

combinari de x-1 luate cate x-3 + aranjamente de x-3 luate cate 2=101

Answer 1

$C_{x-1}^{x-3} +A_{x-3}^{2} =101 \\ \\ C_{x-1}^{x-3} = \frac{(x-1)!}{(x-3)!\cdot2!} = \frac{(x-2)\9x-1)}{1\cdot2} \\ \\ A_{x-3}^{2} = \frac{(x-3)!}{(x-5)!} =(x-4)(x-3)$

$\frac{(x-2)(x-1)}{2}+(x-3)(x-4)=101 \\ \\ x^{2} -x-2x+2+2( x^{2} -3x-3x+12)=202 \\ \\ x^{2} -3x+2+2( x^{2} -7x+12)=202 \\ \\ 3x^{2}-17x+26-202=0$

$3x^{2}-17x-176=0$

3x²-17x-176=0
Δ=b²-4ac=289+4×3×176=289+2112=2401
x₁/₂= (- b+-√Δ)/2a=[17+-√(2401)]/6=(17+-49)/6
x₁=(17+49)/6=66/6 = 11
x₂=(17-49)/6=-32/6 = - 16/3

deci
x₁ = 11
x₂ = - 16/3