Question

Am de rezolvat un sistem de ecuatii cu 2 necunoscute:

$1,339*(a+b) ^{2}+0,037a*(a+b)-1,115a^{2} +0,1617*(a+b)-0,226a-1,178=0$1,1915*(a+b)+1,045a-1,178=0[/tex]

Ma puteti ajuta cu rezolvarea acestui sistem??

Answer 1

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

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

$0,261 a^{2} +2,715ab+1,339b^{2}-0,0643a+0,1617b-1,178$

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

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

$2,2365a+1,1915b=1,178$

$1,1915b=1,178-2,2365a$

$b= \frac{1,178-2,2365a}{1,1915}$

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

$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+$$\frac{0,1904-0,3616a}{1,1915} -1,178=0$

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

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

$-0,1667a ^{2} -3,6755a+0,3212=0 |*(-1)$

$0,1667a ^{2} +3,6755a-0,3212=0$

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

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

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

$a_{1} =0,0870$

$b_{1}= \frac{1,178-2,2365*0,0780}{1,1915}=0,8422$

$a_{2} =<span>-22,1356</span><span>$

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