(17/15) x (17/15) + (2/15) x (2/15) - (17/15) x (4/15) is equal to

Question

\(\frac{17}{15}\times\)\(\frac{17}{15}+\)\(\frac{2}{15}\times\)\(\frac{2}{15}-\)\(\frac{17}{15}\times\)\(\frac4{15}\) is equal to

(a) 0 

(b) 1 

(c) 10 

(d) 11

Answer 1

(b) 1

Given exp. = \(\frac{17}{15}\times\)\(\frac{17}{15}+\)\(\frac{2}{15}\times\)\(\frac{2}{15}-\)2 x \(\frac{17}{15}\times\)\(\frac{2}{15}\)

= \(\big(\frac{17}{15}\big)^2\) + \(\big(\frac{2}{15}\big)^2\) - 2 x \(\frac{17}{15}\times\)\(\frac{2}{15}\)

= \(\big(\frac{17}{15}-\frac{2}{15}\big)^2\)          [Using a² + b² - 2ab = (a - b)²]

= \(\big(\frac{15}{15}\big)^2\) = 1² = 1