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Ex 4.3, 7 - Difference of squares of two numbers is 180 - Ex 4.3

Ex 4.3, 7 - Chapter 4 Class 10 Quadratic Equations - Part 2
Ex 4.3, 7 - Chapter 4 Class 10 Quadratic Equations - Part 3

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Ex 4.3 ,7 The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers. Let larger number be x Given, The square of the smaller number is 8 times the larger number (Smaller number)2 = 8 × Larger number (Smaller number)2 = 8x Smaller number = ±√8𝑥 Also, given that Difference of squares of two numbers is 180 ∴ Square of larger number – square of smaller number = 180 (Larger number)2 – (Smaller number)2 = 180 x2 – (Smaller number)2 = 180 x2 – (√8𝑥 )^2 = 180 x2 – 8x = 180 x2 – 8x – 180 = 0 We factorize using splitting the middle term method x2 + 10x – 18x – 180 = 0 x (x + 10) – 18 (x + 10) = 0 (x – 18) (x + 10) = 0 So, x = 18 and x = – 10 are the roots of the equation Taking x = 18 Larger number = x = 18 & Smaller number = ±√8𝑥 = ±√(8 ×18) = ±√144 = ±√(〖12〗^2 ) = ± 12 Taking x = – 10 Larger number = x = – 10 & Smaller number =±√8𝑥 =±√(8(−10) ) =±√(−80) Since we cannot have negative number in roots x = – 10 is not possible So, our two numbers are 18 & 12 And 18 & −12

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.