Question

If (x1,y1) and (x2,y2) are two ordered pair which satisfies the condition in comprehension (where x1,x2,y1,y2/ϵN),  then (x1x2)/(y1y2) is  20 √500 10 √1000

Solution

The correct option is D √1000 If a, b, c, d are four terms in G.P. then loga, logb, logc and logd are in A.P. ∴log10x,log210x,log210y,log210(xy), in A.P. ⇒log210(xy),−log210y−log210x,    …(i) Also log210y−log210x,=log210x−log210x,    …(2) ∴form(1) (log10x+log10y)(log10x−log10y)=log210y−log210x(log10x+2log10y)(log10x)=log210y−log210x⇒log210y−2log10y.log10x−2log210x=0   …(3)from(2) log210y−2log210x+log10x=0     …(4)(3)−(4)⇒2log10y.log10x−log10x=0 ⇒x=1 or y=1√10 Now, if x=1⇒y=1 Also, if x=1⇒y=1 Also, if y=1√10⇒2log210x=log10x−14=0 logx10x=1±√1+24=1±√34⇒x=x1±√34=1±√34 ⇒x=x1±√34⇒(1,1),(101+√34,1√10)(101−√34,1√10) are three ordered pair

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