Toán Lớp 7: x² +x +6 tìm GTNN nha giúp ik nha

Question

Toán Lớp 7:  x² +x +6 tìm GTNN nha    giúp ik nha

thuminhthong · Answer

$x^2+x+6  =x^2+2.x. dfrac{1}{2}+ dfrac{1}{4}+ dfrac{23}{4}  = left(x^2+2.x. dfrac{1}{2}+ dfrac{1}{4} right)+ dfrac{23}{4}  = left(x+ dfrac{1}{2} right)^2+ dfrac{23}{4}$   Ta có: $ left(x+ dfrac{1}{2} right)^2 ge 0$   $&harr; left(x+ dfrac{1}{2} right)^2+ dfrac{23}{4} ge  dfrac{23}{4}$   $&rarr;$ D&acirc;́u '=' xảy ra khi $x+ dfrac{1}{2}=0$   $&harr;x=- dfrac{1}{2}$   V&acirc;̣y bi&ecirc;̉u thức $x^2+x+6$ đạt GTNN là $ dfrac{23}{4}$ khi $x=- dfrac{1}{2}$

tuenhioanh · Answer

$x&sup2; +x +6$     $=(x&sup2;+2.x. frac{1}{2}+ frac{1}{4})+ frac{3}{4}+5$     $=(x+ frac{1}{2})&sup2;+ frac{23}{4}$     do $(x+ frac{1}{2})&sup2;$&ge;0&forall;x     &rArr;$(x+ frac{1}{2})&sup2;+ frac{23}{4}&ge;0+ frac{23}{4}&forall;x$     Vậy Min =$  frac{23}{4}$ khi $x+ frac{1}{2}=0$                                                 $&rArr;x= frac{-1}{2}$