ALGEBRA Niccolo Fontana Tartaglia was an Italian mathematician , engineer, surveyor and bookkeeper from then Republic of Venice (now Italy). He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs; his work was later validated by Galileo’s studies on falling bodies. Tartaglia along with Cardano were credited for finding methods to solve any third degree polynomials called cubic equations .
He also provided a nice formula for calculating volume of any tetrahedron using distance between pairs of its four vertices. “A person who can, within a year, solve x = is amathematician” - Brahmagupta Niccolo Fontana Tartaglia / – AD(CE) The term “Algebra” has evolved as a misspelling of the word ‘al-jabr’ from one of the important work titled Al-Kitāb al-mukhtaşar fī hisāb al-jabr wa’l-muqābala (“The Compendious Book on Calculation by Completion and Balancing”) written by Persian Mathematician Al-Khwarizmi of th Century AD(CE) Since Al-Khwarizmi’s Al-Jabr book provided the most appropriate methods of solving equations, he is hailed as “ Father of Algebra ”. In the earlier classes, we had studied several important concepts in Algebra. In this class, we will continue our journey to understand other important concepts which will be of much help in solving problems of greater scope.
Real understanding of these ideas will benefit much in learning higher mathematics in future classes. Simultaneous Linear Equations in Two Variables Let us recall solving a pair of linear equations in two variables. Definition Linear Equation in two variables Any first degree equation containing two variables x and y is called a linear equation in two variables. The general form of linear equation in two variables x and y is ax + by + c = , where atleast one of a, b is non-zero and a, b, c are real numbers.
Note that linear equations are first degree equations in the given variables. Example . The father’s age is six times his son’s age. Six years hence, the age of father will be four times his son’s age.
Find the present ages (in years) of the son and father. Solution Let the present age of father be x years and the present age of son be y years Given, x = … ( ) … ( ) Substituting ( ) in ( ) , Þ y = Therefore, son’s age = years and father’s age = years. Example . Solve , x = Solution … ( ) = … ( )