The product of the first three terms of a GP is 8 and the sum of the product of the - Maths - Sequences and Series

Question

The product of the first three terms of a GP is 8 and the sum of
the product of the numbers taken in pairs is 14 Find the numbers no
links pls

Neha Sethi · Accepted Answer

Dear student
Let the three terms in GP be ar,a,arar×a×ar=8⇒a3=8⇒a=2and ar×a+a×ar+ar×ar=14  given⇒a2r+a2r+a2=14⇒a21r+r+1=14⇒1r+r+1=144⇒1+r2+rr=144⇒4+4r2+4r=14r⇒4r2+4r-14r+4=0⇒4r2-10r+4=0⇒2r2-5r+2=0⇒2r2-4r-r+2=0⇒2rr-2-1r-2=0⇒2r-1r-2=0⇒r=2,r=12When a=2 and r=2the three numbers are 22,2,2×2=1,2,4When a=2, r=12the three numbers are 212,2,2×12=4,2,1
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The product of the first three terms of a GP is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers.no links pls