Sum of the squares of the distinct roots of the equation log 2 x ⋅ log 3 x ⋅ log 5 x= log 2 x ⋅ log 3 x+ log 3 x ⋅ log 5 x+ log 5 x ⋅ log 2 x

Question

Sum of the squares of the distinct roots of the equation log 2 x ⋅ log 3 x ⋅ log 5 x= log 2 x ⋅ log 3 x+ log 3 x ⋅ log 5 x+ log 5 x ⋅ log 2 x (A) 960 (B) 961 (C) 900 (D) 901

Tardigrade Admin · Accepted Answer

Roots of equation x = 1, 30 Sum of squares = 1 + 900 = 901

Q. Sum of the squares of the distinct roots of the equation $lo g_{2} x \cdot lo g_{3} x \cdot lo g_{5} x = lo g_{2} x \cdot lo g_{3} x + lo g_{3} x \cdot lo g_{5} x + lo g_{5} x \cdot lo g_{2} x$

960

961

900

901

Roots of equation
$x = 1, 30$
Sum of squares $= 1 + 900 = 901$

Q. Sum of the squares of the distinct roots of the equation log2​x⋅log3​x⋅log5​x=log2​x⋅log3​x+log3​x⋅log5​x+log5​x⋅log2​x

960

961

900

901

Roots of equation x=1,30 Sum of squares=1+900=901

Q. Sum of the squares of the distinct roots of the equation $lo g_{2} x \cdot lo g_{3} x \cdot lo g_{5} x = lo g_{2} x \cdot lo g_{3} x + lo g_{3} x \cdot lo g_{5} x + lo g_{5} x \cdot lo g_{2} x$

Roots of equation
$x = 1, 30$
Sum of squares $= 1 + 900 = 901$