If the set of all a R , for which the equation 2 x^2+(a-5) x+15=3 a has no real root, is the interval ( , ) , and X= x Z: x , then _ x X x^2 is equal to :

Step-by-step solution

aligned & (a-5)^2-8(15-3 a) < 0 & a^2+14 a+25-120 < 0 & a^2+14 a-95 < 0 & (a+19)(a-5) < 0 & a (-19,5) & -19 < x < 5 & _ x X x^2= (1^2+2^2+ .+4^2 )+ (1^2+2^2+ +18^2 ) & = 4 5 9 6 + 18 19 37 6 & =30+2109 & =2139 aligned