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a fost răspuns

Am de rezolvat un sistem de ecuatii cu 2 necunoscute:

[tex]1,339*(a+b) ^{2}+0,037a*(a+b)-1,115a^{2} +0,1617*(a+b)-0,226a-1,178=0

[/tex]1,1915*(a+b)+1,045a-1,178=0[/tex]

Ma puteti ajuta cu rezolvarea acestui sistem??


Răspuns :

[tex]1,339(a ^{2}+2ab+b ^{2} )+0,037 a^{2} +0,037ab-1,115 a^{2} +0,1617a+[/tex][tex]0,1617b-0,226a-1,178=0[/tex]

[tex]1,339a ^{2}+2,678ab+1,339b ^{2} +0,037 a^{2} +0,037ab-1,115 a^{2} +0,1617a[/tex][tex]+0,1617b-0,226a-1,178=0 [/tex]

[tex]0,261 a^{2} +2,715ab+1,339b^{2}-0,0643a+0,1617b-1,178[/tex]

[tex]1,1915a+1,1915b+1,045a-1,178=0[/tex]

1,1915a+1,1915b+1,045a-1,178=0

[tex]2,2365a+1,1915b=1,178[/tex]

[tex]1,1915b=1,178-2,2365a[/tex]

[tex]b= \frac{1,178-2,2365a}{1,1915}[/tex]

[tex]0,261a ^{2}+2,715a* \frac{1,178-2,2365a}{1,1915} +1,339*(\frac{1,178-2,2365a}{1,1915}) ^{2}-0,0643a+[/tex][tex]0,1617*\frac{1,178-2,2365a}{1,1915}-0,226a-1,178=0[/tex]

[tex]0,261 a^{2}+ \frac{3,1982a-6,0720a ^{2}}{1,1915} +1,339* \frac{1,3876-5,2691a+5,0019a ^{2} }{1,1915 ^{2} }-0,0643a+[/tex][tex] \frac{0,1904-0,3616a}{1,1915} -1,178=0[/tex]

[tex]0,261* 1,1915^{2} +1,1915*( 3,1982a-6,0720a^{2})+1,8579-7,0553a+[/tex][tex]6,6975 a^{2} -0,0645*(1,1915) ^{2}+1,1915*(0,1904-0,3616a)-1,178[/tex][tex]*(1,1915) ^{2}=0[/tex]

[tex]0,3705 a^{2} +3,8106a-7,2347 a^{2} +1,8579-7,0553+6,6975a^{2}-[/tex][tex]0,0912+0,2268-0,4308a-1,6723[/tex]

[tex]-0,1667a ^{2} -3,6755a+0,3212=0 |*(-1)[/tex]

[tex]0,1667a ^{2} +3,6755a-0,3212=0[/tex]

[tex]Δ= b^{2} -4ac=(3,6755) ^{2} -4*0,1667*(-0,3212)=13,5093+0,2141[/tex][tex]=13,7234[/tex]

[tex] a_{1} = \frac{-b+ \sqrt{Δ} }{2a} = \frac{-3,6755+ \sqrt{13,7234} }{2*0,1667} =0,0870[/tex]

[tex] a_{2} = \frac{-b- \sqrt{Δ} }{2a} = \frac{-3,6755- \sqrt{13,7234} }{2*0,1667} =-22,1356[/tex]

[tex]a_{1} =0,0870[/tex]

[tex]b_{1}= \frac{1,178-2,2365*0,0780}{1,1915}=0,8422[/tex]

[tex]a_{2} =-22,1356[/tex]

[tex]b_{2}=\frac{1,178-2,2365*(-22,1356)}{1,1915}=17,6895[/tex]