2) Solve: 52 − − 15 = 0 by using factarisation method.
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ꜱᴡᴇʀ:
(1) x2 + 5x – 2 = 0
ᴏɴʟy ᴏɴᴇ ᴠᴀʀɪᴀʙʟᴇ x.
ᴍᴀxɪᴍᴜᴍ ɪɴᴅᴇx = 2
ꜱᴏ, ɪᴛ ɪꜱ ᴀ qᴜᴀᴅʀᴀᴛɪᴄ ᴇqᴜᴀᴛɪᴏɴ.
(2) y2 = 5y – 10
ᴏɴʟy ᴏɴᴇ ᴠᴀʀɪᴀʙʟᴇ y.
ᴍᴀxɪᴍᴜᴍ ɪɴᴅᴇx = 2
ꜱᴏ, ɪᴛ ɪꜱ ᴀ qᴜᴀᴅʀᴀᴛɪᴄ ᴇqᴜᴀᴛɪᴏɴ.
(3) y2+1y=2
⇒y3+1=2y
ᴏɴʟy ᴏɴᴇ ᴠᴀʀɪᴀʙʟᴇ y.
ᴍᴀxɪᴍᴜᴍ ɪɴᴅᴇx = 3
ꜱᴏ, ɪᴛ ɪꜱ ɴᴏᴛ ᴀ qᴜᴀᴅʀᴀᴛɪᴄ ᴇqᴜᴀᴛɪᴏɴ.
(4) x+1x=-2
⇒x2+1=-2x
ᴏɴʟy ᴏɴᴇ ᴠᴀʀɪᴀʙʟᴇ x.
ᴍᴀxɪᴍᴜᴍ ɪɴᴅᴇx = 2
ꜱᴏ, ɪᴛ ɪꜱ ᴀ qᴜᴀᴅʀᴀᴛɪᴄ ᴇqᴜᴀᴛɪᴏɴ.
(5) (ᴍ + 2) (ᴍ – 5) = 0
⇒ᴍ2-3ᴍ-10=0
ᴏɴʟy ᴏɴᴇ ᴠᴀʀɪᴀʙʟᴇ ᴍ.
ᴍᴀxɪᴍᴜᴍ ɪɴᴅᴇx = 2
ꜱᴏ, ɪᴛ ɪꜱ ᴀ qᴜᴀᴅʀᴀᴛɪᴄ ᴇqᴜᴀᴛɪᴏɴ.
(6) ᴍ3 + 3ᴍ2 – 2 = 3ᴍ3
ᴏɴʟy ᴏɴᴇ ᴠᴀʀɪᴀʙʟᴇ ᴍ.
ᴍᴀxɪᴍᴜᴍ ɪɴᴅᴇx = 3
ꜱᴏ, ɪᴛ ɪꜱ ɴᴏᴛ ᴀ qᴜᴀᴅʀᴀᴛɪᴄ ᴇqᴜᴀᴛɪᴏɴ.
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