Question

A man bought y pencils at Rs. x. If the price of each pencil be one rupee less, he could get

one more pencil for the same money.
Show that 
$2y = \sqrt{1 + 4x} - 1$
[Please help me.. I will mark as brainliest]
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Answer 1

✪ᴀɴsᴡᴇʀ✪

☆ɢɪᴠᴇɴ☆

• A man buys 'y' pencils with Rs.'x'.

• If cost of a pencil is 1 rupee less, he could buy one more pencil with the same amount.

☆ᴛᴏ ᴘʀᴏᴠᴇ☆

• $2y = \sqrt{1 + 4x} - 1$

☆ᴘʀᴏᴏғ☆

• Original cost of one pencil $= \frac{x}{y}$

• If the cost of one pencil is 1 rupee less i. e. $\left(\frac{x}{y}-1\right)$, he could buy one more pencil i. e. $(y+1)$ pencils with Rs. x. Thus

$\:\:\:\:\:\:\:\:\left(\frac{x}{y}-1\right)(y+1) = x$

$\implies x + \frac{x}{y} -y - 1 = x$

$\implies \frac{x}{y} -y - 1 = 0$

$\implies x -y^2 - y = 0$

$\implies y^2 + y - x = 0$

$\implies y =\frac{-1±\sqrt{1^2 - 4.1.(-x)}}{2.1}$

Since y cannot be negative,

$\implies y =\frac{-1+\sqrt{1 +4x}}{2}$

$\implies 2y = \sqrt{1 +4x} - 1$

Hence Proved.

Answer 2

I have mentioned my answer above please Mark me as brainliest