Question

divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164. AND ALSO PLS SAY FROM WHICH BOOK THIS TYPE OF QUESTIONS IS ASKED​

Answer 1

卂几丂山乇尺

ᴅɪᴠɪᴅᴇ 16 ɪɴᴛᴏ ᴛᴡᴏ ᴘᴀʀᴛs ʟᴇᴛ x ɪs ʟᴏɴɢᴇʀ ᴘᴀʀᴛ ᴀɴᴅ

(16-x ) ɪs sᴍᴀʟʟᴇʀ ᴘᴀʀᴛ

ᴀᴄᴏᴜʀᴅɪɴᴅ ᴛᴏ ϙᴜᴇᴛɪᴏɴ:-

\ʙᴇɢɪɴ{ʟɢᴀᴛʜᴇʀᴇᴅ}2 \ᴛɪᴍᴇs {x}^{2} = {(16 - x)}^{2} + 164 \\ 2 {x}^{2} = 256 + {x}^{2} - 32x + 164 \\ {x}^{2} + 32x - 420 = 0\\ {x}^{2} + 42x - 10x - 420 = 0 \\ x(x + 42) - 10(x + 42) = 0\\ (x + 42)(x - 10) = 0 \\ x = - 42 \: ᴅᴏᴇs \: ɴᴏᴛ \: ᴇxɪᴛs \\ (x = 10 ) \: ʟᴏɴɢᴇʀ \: ᴘᴀʀᴛ \\ (16 - x) = (16 - 10) \\ 6 \: ɪs \: sᴍᴀʟʟᴇʀ \: ᴘᴀʀᴛ \\ 10 \: ɪs \: ʟᴏɴɢᴇʀ \: ᴘᴀʀᴛ \\\ᴇɴᴅ{ʟɢᴀᴛʜᴇʀᴇᴅ}2×x2=(16−x)2+1642x2=256+x2−32x+164x2+32x−420=0x2+42x−10x−420=0x(x+42)−10(x+42)=0(x+42)(x−10)=0x=−42ᴅᴏᴇsɴᴏᴛᴇxɪᴛs(x=10)ʟᴏɴɢᴇʀᴘᴀʀᴛ(16−x)=(16−10)

6ɪssᴍᴀʟʟᴇʀ ᴘᴀʀᴛ 10 ɪs ʟᴏɴɢᴇʀ ᴘᴀʀᴛ