Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 206443 by Safojon last updated on 14/Apr/24

Commented by necx122 last updated on 15/Apr/24

getting a more detailed solution will be excellent for us. I still tried going through the solution already done but I couldn't understand the approaches readily. Please, whoever can expound would be a help. Thanks.

Commented by A5T last updated on 15/Apr/24

$$Let\mathit{u}=(a,b,c);\mathit{v}=(x,y,z)$$$$Then\mathit{u}\cdot \mathit{v}⩽\mid \mathit{u}\mid \mid \mathit{v}\mid (equalitywhen\mathit{u}=\lambda \mathit{v})$$$$\Rightarrow ax+by+cz⩽\sqrt{a^2+b^2+c^2}\sqrt{x^2+y^2+z^2}=30$$$$\Rightarrow ax+by+cz=30whenequalityholds$$$$\Rightarrow (a,b,c)=(\lambda x,\lambda y,\lambda z)\Rightarrow ax+by+cz=30$$$$\Rightarrow \lambda (x^2+y^2+z^2)=\lambda \left(36\right)=30\Rightarrow \lambda =\frac{30}{36}=\frac{5}{6}$$$$\Rightarrow \frac{a+b+c}{x+y+z}=\frac{\lambda (x+y+z)}{x+y+z}=\lambda =\frac{5}{6}$$

Commented by MATHEMATICSAM last updated on 14/Apr/24

$$\mathrm{Q}193296$$

Commented by necx122 last updated on 16/Apr/24

Wow!!! I've been able to solve along and understand. Thanks to everyone that attempted this problem.

Terms of Service

Privacy Policy

Contact: info@tinkutara.com