Question:
If a3 + b3 + c3 = 62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac ?
If a3 + b3 + c3 = 62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac ?
Updated On: Jul 21, 2025
- 3
- 4
- 5
- 6
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
We know, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
52 = a2 + b2 + c2 + 2(ab + bc + ac)
a2 + b2 + c2 = 25 - 2(ab + bc + ac)) …. (i)
a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2 - ab - bc - ac) + 3abc
62 = 5 * (25 - 2(ab + bc + ac) - (ab + bc + ac)) + 3 * (-6) (from (i))
ab + bc + ac = 3
So, the correct option is (A) : 3.
52 = a2 + b2 + c2 + 2(ab + bc + ac)
a2 + b2 + c2 = 25 - 2(ab + bc + ac)) …. (i)
a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2 - ab - bc - ac) + 3abc
62 = 5 * (25 - 2(ab + bc + ac) - (ab + bc + ac)) + 3 * (-6) (from (i))
ab + bc + ac = 3
So, the correct option is (A) : 3.
Was this answer helpful?
0
0
Top Questions on Algebra
If the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) has equal roots, where \( a + c = 15 \) and \( b = \frac{36}{5} \), then \( a^2 + c^2 \) is equal to .
- Find the value of \( x \) in the equation \( 5x - 7 = 3x + 9 \).
- Find the value of \( x \) in the equation \( 2x + 3 = 7x - 8 \).
- Find the value of \( x \) in the equation \( 4x - 2 = 10 \).
- Solve the quadratic equation: \[ x^2 - 5x + 6 = 0 \]
View More Questions
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle ADE\) is
- CAT - 2024
- Mensuration
When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
- CAT - 2024
- Mensuration
- Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
- CAT - 2024
- Time and Work
View More Questions