Find the values of the following expressions: (i) 16x^2+24x+9, when x = 7/4 (ii) 64x^2+81y^2+144xy, when x = 11 and y = 4/3

Question

Find the values of the following expressions:

(i) 16x² + 24x + 9, when x = \(\frac{7}{4}\)

(ii) 64x² + 81y² + 144xy, when x = 11 and y = \(\frac{4}{3}\)

(iii) 81x² + 16y² - 72xy, when x = \(\frac{2}{3}\) and y = \(\frac{3}{4}\)

Answer 1

(i)  16² + 24x + 9, when x = \(\frac{7}{4}\)

(4x)² + 2 (4x) (3) + 3²

= (4x + 3)²

Putting x = \(\frac{7}{4}\)

= [4 (\(\frac{7}{4}\)) + 3]²

= (7 + 3)²

= 100

(ii)  64² + 81y² + 144xy, when x = 11 and y = \(\frac{4}{3}\)

(8x)² + 2 (8x) (9y) + (9y)²

= (8x + 9y)²

Putting x = 11 and y = \(\frac{4}{3}\)

= [8 (11) + 9 (\(\frac{4}{3}\))]²

= (88 + 12)²

= (100)²

= 10000

(iii)  81x² + 16y² - 72xy, when x = \(\frac{2}{3}\) and y = \(\frac{3}{4}\)

(9x)² + (4y)² – 2 (9x) (4y)

= (9x – 4y)²

Putting x = \(\frac{2}{3}\) and y = \(\frac{3}{4}\)

= [9 (\(\frac{2}{3}\)) – 4 (\(\frac{3}{4}\))]²

= (6 – 3)²

= 3²

= 9