Oblicz wyraz pierwszy a1 i różnicę r ciągu arytmetycznego (an), jeżeli: h)[latex] left { {{a_9 + a_1_2} =40} atop {a^{2}_1_5 - a^{2}_1_1=400}} ight. [/latex] (jak coś to jest a15 do kwadratu i a11 do kwadratu)

[latex] left { {{a _{9} + a_{12} =40} atop {a _{15} ^{2} -a _{11} ^{2} =400 }} ight. \ left { {{a _{1}+8r+ a_{1}+11r=40 } atop {( a_{1} +14r) ^{2}-( a_{1} +10r) ^{2} =400 }} ight. \ 2a _{1} =40-19r \ a_{1} =20-9,5r \ (20-9,5r+14r) ^{2} -( 20-9,5r+10r) ^{2} =400 \ (20+4,5r) ^{2} -(20+0,5r) ^{2} =400 \ 400+180r+20,25r ^{2} -400-20r-0,25r ^{2} -400=0 \ 20r ^{2} +160r-400=0 \ r^{2} +8r-20=0 [/latex] Δ=64-4·1·(-20)=144 √Δ=12 r₁=[latex] frac{-8+12}{2} =2[/latex] r₂=[latex] frac{-8-12}{2} = -10[/latex] a₁=20-9,5·2=1 v a₁= 20-9,5·(-10)=115 Odp: [latex] left { {{a_{1} =1} atop {r=2}} ight. v left { {{a _{1} =115} atop {r= -10}} ight. [/latex]