If A = (58² - 25²)/(46² - 37²), B = (26² - 15²)/(56² - 15²) then the value of 1/B - 20/A is:

If A = (58² - 25²)/(46² - 37²), B = (26² - 15²)/(56²…

If $A = \frac{58^2 - 25^2}{46^2 - 37^2}, B = \frac{26^2 - 15^2}{56^2 - 15^2}$ then the value of $\frac{1}{B} - \frac{20}{A}$ is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 1.

A = $\frac{58^2−25^2}{46^2−37^2 }$

⇒ A = $\frac{(58 +25)(58-25)}{(46+37)(46-37)}$ = $\frac{33}{9} = \frac{11}{3}$

B = $\frac{26^2−15^2}{56^2−15^2 }$

⇒ B = $\frac{(26-15)(26+15)}{(56-15)(56+15)} = \frac{11}{71}$

Hence $\frac{1}{B} - \frac{20}{A}$ = 1/(11/71) - 20/(11/3)

⇒ 71/11 - 60/11 = 11/11 = 1