Question:medium

If a+b+c=11 and ab + bc + ca = 35, find the value of (a-b)²+(b-c)²+(c-a)².

IBSAT

Updated On: Nov 25, 2025

30
32
35
40
25

Top Questions on Algebra

If \( a, b, c \) are all positive integers, with \( 4a>b \), then which of the following conditions is BOTH NECESSARY AND SUFFICIENT for the expression \[ \sqrt{(3)^a (21)^{3a-b} (49)^{2b+c}} \] to be a positive integer?
View Solution
For how many distinct real values of \( x \) does the equation below hold true? (Consider \( a>0 \)) \[ x^2 \log_a (16) - \log_a (64) \div \log_a (32) - x = 0 \]
View Solution
The market value of beams, made of a rare metal, has a unique property: the market value of any such beam is proportional to the square of its length. Due to an accident, one such beam got broken into two pieces having lengths in the ratio 4:9. Considering each broken piece as a separate beam, how much gain or loss, with respect to the market value of the original beam before the accident, is incurred?
View Solution
In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
\(R\) and \(S\) scored the same on the first test.
From the second test onwards, \(R\) consistently scored the same (a non-zero score).
The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
From the fifth test onwards, \(S\) scored the same as \(R\).
The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in IBSAT exam

The sides of a rectangular field are in the ratio of 3:5 and its area is 2535 m2. Calculate the cost of fencing it at the rate of Rs.2.50/m.

IBSAT
Mensuration

View Solution

What is the length of the longest rod that can be put on the floor of a rectangular room measuring 45 min length and 28 m in breadth?

IBSAT
Mensuration

View Solution

In each of the following questions a number series is given with one missing (?) term. The term is given as one of the alternatives among the five numbers given in the answer choic Find the term.
2, 5,11,23,47,?

IBSAT
Sequence and Series

View Solution

In each of the following questions a number series is given with one missing (?) term. The term is given as one of the alternatives among the five numbers given in the answer choic Find the term.
1, 3, 4, 8, 15, 27, ?

IBSAT
Sequence and Series

View Solution