THE SUM OF A NUMBER X AND ITS RECIPROCAL IS 26/5. WHAT NUMBER IS X?

X+1/X=26/5.

(X^2+1)/X=26/5.

5(X^2+1)=26X.

5X^2-26X+5=0.

By factorisation.

5X^2-25X-X+5=0.

5X(X-5)-1(X-5)=0.

(5X-1)(X-5)=0.

X=5 or 1/5.

Take X=5.