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Najwa123
@Najwa123
April 2019
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Aidez moi
soient a,b,c,d,met n des nombres réels non nuls et tel que mb+nc≠0
montrer que si a/b=c/d alors a/b=c/d=ma+nc/mb+nd
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slyz007
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Puisque a/b=c/d on a aussi a/c=b/d et c/a=d/b
ma+nc=a(m+nc/a)=a(m+nd/b)
mb+nd=b(m+nd/b)
Donc (ma+nc)/(mb+nd)=a/b
De même ma+nc=c(ma/c+n)
et mb+nd=d(mb/d+n)=d(ma/c+n)
Donc (ma+nc)/(mb+nd)=c/d
On a donc bien a/b=c/d=(ma+nc)/(mb+nd)
0 votes
Thanks 1
najwa123
non ce n'est pas clair
najwa123
merci beaucoup
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Lista de comentários
Verified answer
Puisque a/b=c/d on a aussi a/c=b/d et c/a=d/bma+nc=a(m+nc/a)=a(m+nd/b)
mb+nd=b(m+nd/b)
Donc (ma+nc)/(mb+nd)=a/b
De même ma+nc=c(ma/c+n)
et mb+nd=d(mb/d+n)=d(ma/c+n)
Donc (ma+nc)/(mb+nd)=c/d
On a donc bien a/b=c/d=(ma+nc)/(mb+nd)