If 2a = 1 − 2(√a) Find ((2a^2 + (√a))/(2a)) = ?


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 214247 by hardmath last updated on 02/Dec/24

$If 2 a = 1 - 2 \sqrt{a}$ $Find \frac{{2 a}^{2} + \sqrt{a}}{2 a} = ?$
	Answered by A5T last updated on 02/Dec/24
	$2a=1−2(√a)⇒ { (((√a)=((2a−1)/(−2)))),(((2a−1)^2 =4a⇒4a^2 +1=8a)) :} ⇒((2a^2 +(√a))/(2a))=((2a^2 +((2a−1)/(−2)))/(2a))=((−4a^2 +2a−1)/(−4a)) =((−(4a^2 +1)+2a)/(−4a))=((−8a+2a)/(−4a))=(3/2)$
	$2 a = 1 - 2 \sqrt{a} \Rightarrow {\begin{cases} \sqrt{a} = \frac{2 a - 1}{- 2} \\ {(2 a - 1)}^{2} = 4 a \Rightarrow 4 a^{2} + 1 = 8 a \end{cases}$ $\Rightarrow \frac{2 a^{2} + \sqrt{a}}{2 a} = \frac{2 a^{2} + \frac{2 a - 1}{- 2}}{2 a} = \frac{- 4 a^{2} + 2 a - 1}{- 4 a}$ $= \frac{- (4 a^{2} + 1) + 2 a}{- 4 a} = \frac{- 8 a + 2 a}{- 4 a} = \frac{3}{2}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum