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Question Number 74802 by liki last updated on 30/Nov/19

Commented by liki last updated on 30/Nov/19

$$...plzineedhelp;mrwandmrmindispower$$$$,oranyeonetoassistme!$$

Commented by abdomathmax last updated on 30/Nov/19

$$wehavef\left(x\right)=4x^2-4x+4theequationoftangente$$$$yothegraphat{M}_0(x_0,y_0)isy=f^{{}^{\prime }}\left(x_0\right)(x-x_0)+f\left(x_0\right)$$$$\Rightarrow f^{{}^{\prime }}\left(x_0\right)x-f^{{}^{\prime }}\left(x_0\right).x_0-y+f\left(x_0\right)=0\Rightarrow$$$$(8x_0-4)x-(8x_0-4)x_0-y+f\left(x_0\right)=0$$$$thedirectorvectoris\overrightarrow{u}(1,8x_0-4)anddirector$$$$vectorofline8x-y-6=0is\overrightarrow{v}(1,8)wemust$$$$havedet(\overrightarrow{u},\overrightarrow{v})=0\Rightarrow \left|\begin{array}{c}11\\ 8x_0-48\end{array}\right|=0\Rightarrow$$$$8-8x_0+4=0\Rightarrow 2-2x_0+1=0\Rightarrow 3-2x_0=0\Rightarrow$$$$x_0=\frac{3}{2}\Rightarrow f\left(x_0\right)=4{\left(\frac{3}{2}\right)}^2-4\left(\frac{3}{2}\right)+4$$$$=9-6+4=7\Rightarrow A(\frac{3}{2},7)$$

Commented by liki last updated on 01/Dec/19

$$...thankssir..$$

Commented by mathmax by abdo last updated on 01/Dec/19

$$youarewelcome.$$

Answered by mr W last updated on 01/Dec/19

$$Q2:$$$$notclearwhatiszm\mathrm{\_}1andm\mathrm{\_}4?$$$$pleasecheckthequestion.$$$$$$$$Q3:$$$$sayonerootis\alpha ,theotheroneisn\alpha .$$$$\alpha +n\alpha =(n+1)\alpha =-p$$$$\alpha \left(n\alpha \right)=n{\alpha }^2=q$$$$\Rightarrow \alpha =-\frac{p}{n+1}$$$$n\times \frac{p^2}{{(n+1)}^2}=q$$$$\Rightarrow {np}^2={(n+1)}^{2}q$$$$\Rightarrow {np}^2=n^{2}q+2nq+q$$$$\Rightarrow {qn}^2+(2q-p^2)n+q=0$$

Commented by liki last updated on 01/Dec/19

$$...thankyouverymuchsir.$$

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