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ALGEBRA ALGEBRA + + a2)] - = [ta? 2ab +62) +(62 - 2bc + c2) + (c2 – 2ca + a? = [(a - b)2 + (b-cjø +(c = a)*] > 0 Sol. (2) Firstly we have to find the value of xy + y2 + 2x because x2 + y + 2 - 3xyz = (x+y+z) (x+y+z2 - xy - yz-zxd. (x + y + 2)2 = x + y2 + 2 + 2xy + 2yz + 2zx 92 - 35 + 2 (xy + y2 + 2x) 81 - 35 = 2 (xy + y2 + zxd 46 Xy - y2 + 2x = 23 2 . * + y + 28 - 3xyz (x + y + 2) (x2 + y2 + x2 - (xy + y2 + zx)) = 9 (35 - 23) = 9 x 12 = 108 02 + b2 + c -- (ab + bc + ca) >O a bajo > ab + bc + ca + C aa + b2 + c2 ab + bc + ca 16. If p+q+r=9 and pq + gr + rp= 23 then p2 + 2 = م = 2 + 1 13. If x4 + --- 1 = 47, then the value of x + -is : s X = (1)3 (3) +3 (2)-3 Siamo Te up (4)4 1 1 2 4 = x + Sol. (3) X + 2x2 1 x2 *4 up = 47 + 2 = 49 (1) 30 (2) 32 (3) 33 (4) 35 Sol. (4) (+ q + r)2 = p2 + + pe + 2 (pq+ ar + rp) = 81 = p + q2 + 2 + 2 x 23 p> + + p2 = 81 46 = 35 17. If 3a-2b= 11 and ab = 12, then 27a-8b3 = ? (1) 3700 (2) 3707 (3) 3500 Sol. (2) (3a-2b) = (3a) - (2b)3 – 3 3ax 2b (3a-2b) a)3 ) 3505 = 27a-863 - 18ab (3a-2b) 113 = 27a - 8b3 - 18 x 12 x 11 1331 = 27a-8b3-2376 27a-8b3 = 2376 + 1331 = 3707 18. If x(x + y + z) = 20; y (x + y + 2) = 30 and 2(x + y + 2) = 50, then the value of 2 (x + y + z) is : (1) 20 (2)-10 1 -*** )=1732 + 7=ܨ܀ 2> because x = a positive quantity. Again, - + (x+ 2 1 1 X + - = x2 + +2.x. + x x2 x² 1 + 2 x2 + MW.10 1E (ه) 151515- ...
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