1133correction: rounded to nearest integer? and relations should be ≤ and not <
x1, x2, x3, x4 are real nos.
x1 < x2 < x3 < x4.
Product of any three chosen at a time + the remaining = 130.
Find the sum of all possible values of x4 rounded to the nearest decimal place.
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5 Answers
1133
2305Let P=x1x2x3x4
x1+x2x3x4 = 130
x1+Px1=130
Similarly,
x2+Px2=130=x1+Px1
→x1x2 = P = x1x2x3x4
→x3x4=1
Similarly,
x2x3 = 1 = x3x4
→x2 = x4
Similarly we can find that:
x1=x2=x3=x4
Therefore,
x1+x13=130
→x13+x1-130=0
Using vieta's formula,
Sum of roots = -coeffcient of x2coeffcient of x3 = -01=0
Anurag Roy I think it should be (x1)*(x4)=1;(x2)*(x3)=1;that satisfies the condition x1Upvote·0· Reply ·2013-03-24 06:18:26