19) If pth qth and rth terms of a gp are X, Y, Z find value of
x(q-r) ×y(r-p) × z( p-q)
the bracket things are in power to the x y z respect ively
Answers
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Answer:
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Given,
Given,arp−1=x
Given,arp−1=xarq−1=y
Given,arp−1=xarq−1=yarr−1=z
Given,arp−1=xarq−1=yarr−1=z⇒(arp−1)q−r=xq−r
Given,arp−1=xarq−1=yarr−1=z⇒(arp−1)q−r=xq−r⇒(arq−1)r−p=yr−p
Given,arp−1=xarq−1=yarr−1=z⇒(arp−1)q−r=xq−r⇒(arq−1)r−p=yr−p⇒(arr−1)p−q=zp−q
Given,arp−1=xarq−1=yarr−1=z⇒(arp−1)q−r=xq−r⇒(arq−1)r−p=yr−p⇒(arr−1)p−q=zp−qxq−ryr−pzp−q=(arp−1)q−r(arq−1)r−p(arr−1)p−q
Given,arp−1=xarq−1=yarr−1=z⇒(arp−1)q−r=xq−r⇒(arq−1)r−p=yr−p⇒(arr−1)p−q=zp−qxq−ryr−pzp−q=(arp−1)q−r(arq−1)r−p(arr−1)p−qxq−rxyr−pxzp−q=a(p+q+r−p−q−r)r(pq+qr+rp+p+q+r−qp−rq−pr−p−q−r)
Given,arp−1=xarq−1=yarr−1=z⇒(arp−1)q−r=xq−r⇒(arq−1)r−p=yr−p⇒(arr−1)p−q=zp−qxq−ryr−pzp−q=(arp−1)q−r(arq−1)r−p(arr−1)p−qxq−rxyr−pxzp−q=a(p+q+r−p−q−r)r(pq+qr+rp+p+q+r−qp−rq−pr−p−q−r)⇒xq−rxyr−pxzp−q=a0r0
Given,arp−1=xarq−1=yarr−1=z⇒(arp−1)q−r=xq−r⇒(arq−1)r−p=yr−p⇒(arr−1)p−q=zp−qxq−ryr−pzp−q=(arp−1)q−r(arq−1)r−p(arr−1)p−qxq−rxyr−pxzp−q=a(p+q+r−p−q−r)r(pq+qr+rp+p+q+r−qp−rq−pr−p−q−r)⇒xq−rxyr−pxzp−q=a0r0∴xq−rxyr−pxzp−q= 1.
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