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Most Important Algebra Question For Competition Exam ~ Crack Now

1.यदि  x-1x,तब  x3-1x3 किसके बराबर है ?


solution - 


given thant x-1x=6
                 
                 à¤¦à¥‹à¤¨à¥‹à¤‚ और घन करने पर 
(x-1x)3=63
x3-1x3-3×x×1x(x-1x)=216 [ SSC CPO SI 2019]
x3-1x3-3(x-1x)=216
x3-1x3-3×6=216
x3-1x3-18=216
x3-1x3=216+18
x3-1x3=234


2. यदि a3+b3=5824  और   a+b=28  तो  (a-b)2+a×b = ?

given a3+b3=5824  और   a+b=28
a3+b3=5824  ----------(1)
a+b=28    -------------(2)
on taking cubes bothsides we have 
(a+b)3=283
a3+b3+3×a×b×(a+b)=21952 from equation 1 
5824+3×ab×28=21952       from equation 2
84×ab=21952-5824
84×ab=16128
ab=192----------------(3)
 now squaring equation no 2 we have 
(a+b)2=282
a2+b2+2×ab=784
a2+b2+2×192=784
a2+b2+384=784
a2+b2=784-384
a2+b2=400--------------(4)

now 
(a-b)2+ab
=a2+b2-2×ab+ab
=a2+b2-ab from equation 3 & 4
=400-192
=208



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