1.यदि x-1x,तब x3-1x3 किसके बराबर है ?
solution -
given thant x-1x=6
दोनों 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
Tags
Mathematics