Logarithm Question (Important)

Please help me for answered this question

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

$P=2X^2+(3-X)^2$ ) Minimum of P is at $X=1$ or $(x,y)=(2,4)$ which is $6$

Aditya Parson - 8 years, 1 month ago

from what P=2X^2+(3−X)^2 ?

Fadlan Semeion - 8 years, 1 month ago

The questions asks us to express P in terms of X.

Aditya Parson - 8 years, 1 month ago

@Aditya Parson – i understood about 2x^2, but i have question, from what (3−X)^2 ?

Fadlan Semeion - 8 years, 1 month ago

@Fadlan Semeion – it is given xy=8 so you can derive y in terms of X as well.

Aditya Parson - 8 years, 1 month ago

I thought the minimum of P is 6 because from the equation P=2X^2 + (3-X)^2=3X^2-6X+9 by completing the square P=3(X-1)^2 + 6, hence the minimum value is 6. Even if we consider your answer that 0 is minimum then log x base 2 has to be zero > then x=1 and repeating the same argument we find that y=1 and unfortunately this contradicts the statement that xy=8 because if minimum P is 0 then xy has to be 1.

Pralhlad Hardman - 8 years, 1 month ago

You are right.

Aditya Parson - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$