Toughest Math Problem

Introduction to toughest math problem

Mathematics is a subject that consists of various different topics with different models of problems. Mathematics consists of both toughest math problems and also some easier problems. Toughest math problem mostly comes under the topics of trigonometry, calculus, analytical geometry, Measurements, integration, Probability etc. toughest problems are solved with more number of steps and various formulas in the problem.Toughest math problem basically comes under higher grades and college grades.

Example of Toughest Math Problem

1. Solve the equations: p + 2q + 3r = 14, 3p + q + 2r = 11, 2p + 3q + r = 11.

Solution: Let the given equations be identified as follows:

p + 2q + 3r = 14------- (1)

3p + q + 2r = 11------ (2)

2p + 3q + r = 11------ (3)

Consider the equations (1) and (3)

(1) ⇒ p + 2q + 3r = 14

(3) × 3 ⇒ 6p + 9q + 3r = 33 subtracting

–5p – 7q = –19

5p + 7q = 19 (4)

Consider the equations (2) and (3)

(2) ⇒ 3p + q + 2r = 11

(3) × 2 ⇒ 4p + 6q + 2r = 22 subtracting

–p – 5q = –11

p + 5q = 11 (5)

Consider the equations (4) and (5)

(4) ⇒ 5p + 7q = 19

(5) × 5 ⇒ 5p + 25q = 55 subtracting

–18q = –36; ∴q = 2

Substitute q = 2 in (5) we get

p + 5(2) = 11; p + 10 = 11; ∴p= 1

Substitute p = 1, q = 2 in (3) we get

2(1) + 3(2) + r = 11; 2 + 6 + r = 11 ⇒ r = 3

The solution is p = 1, q = 2, r = 3.

Practice the Toughest Math Problem

1. Solve: 3a – 3b + 4c = 14; –9a – 6b + 2c = 1; 6a + 3b + c = 5

Answer: The solution is a = 1, b = –1, c = 2

2. Solve: l+ m = 3, m + n = –5, n + l = 2.

Answer: The solution is l = 5, m = –2, n = –3.