1.

If 4 x^2 +9 y^2= 69 and xy=1 find 2x+3y​

Answer»

Given:

  • 4x² + 9y² = 69
  • xy = 1

To find:

  1. 2X + 3y = ?

Method:

Squaring (2x + 3y) and expand it using

(a + B)² = a² + b² + 2ab

(2x + 3y)² = (2x)² + (3y)² + 2(2x)(3y)

⇒ (2x + 3y)² = 4x² + 9y² + 12xy

⇒ (2x + 3y)² = 69 + 12(1)

⇒ (2x + 3y)² = 69 + 12

⇒ (2x + 3y)² = 81

⇒ (2x + 3y) = √81

⇒ (2x + 3y) = 9


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