Page 120 - Grade 10 C.Math

9.4. ;fwf/0f d"ns ;dLs/0f (Equations involving surds)

√16 eGgfn] s] a'lemG5 < s] √x = x n]Vg ;lsG5 < 5nkmn ug'{xf];\ .

rn/flz dn;lxt ePsf] ;dLs/0fnfO{ ;fwf/0f d"ns ;dLs/0f elgG5 . pbfx/0fsf
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nflu √x = 2, √x − 1 = 5 cflb . d"n lrxgsf] ju{ ubf{ d"n lrxg x6\5, h:t M
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Curriculum Development Centre

√x = 3 eP √x = (3) cyjf = 9 x'G5 .
;fwf/0f d"ns ;dLs/0f xn ubf{ k|fKt ePsf] pTt/ l7s 5 5}g egL yfxf kfpg pTt/
k|lt:yfkg u/L x]g{ ;lsG5 . ;fwf/0fd"ns ;dLs/0f xn ubf{ k|fKt x'g] ;ªVofx¿dWo]
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h'g ;ªVofn] ;dLs/0fnfO{ ;Gti6 ub}{g To;nfO "Extraneous root" eGb5g .
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pbfx/0f

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1. xn ugxf];\ -s_ √x + 5 − √x = 1 -v_ √ + 1 = 3
;dfwfg

-v_ oxfF, √ + 1 = 3
-s_ oxfF, √x + 5 − √x = 1

cyjf, √ = 3 − 1
cyjf, √x + 5 = 1 + √x

cyjf, √ = 2

cyjf, √x + 5 = 1 + √x -b'j}lt/ ju{ ubf{_

cyjf, x + 5 = 1 + 2√x + x cyjf, = 2
cyjf, 4 = 2√x b'j}lt/ rf}yf] 3ft lnFbf

cyjf, 2 = √x ×
cyjf, = 16
2
2
cyjf, (2) = √x
cyjf, = 16
cyjf, 4 = x
hfFr ubf{ M
hfFr ubf{, √x + 5 − √x = 1

√ + 1 = 3
cyjf, √4 + 5 − √4 = 1

cyjf, √16 + 1 = 3
cyjf, 3 − 2 = 1
cyjf, 2 + 1 = 3
cyjf, 1 = 1
cyjf, 3 = 3
∴ x = 4
 x = 16

ul0ft, sIff – 10 117