Dehli Police Constable Model Paper 5 (HM)

दिया है​​:
a + b = 7
ab = 10
${\mathit{a}}^3\mathit{–}{\mathit{b}}^3$ = 117
उपयोग किया गया सूत्र​:
${\left(\mathit{a}+\mathit{b}\right)}^2$ = ${\mathit{a}}^2+{\mathit{b}}^2$ + 2ab
${\mathit{a}}^3\mathit{–}{\mathit{b}}^3$ = (a – b) $\left({\mathit{a}}^2+{\mathit{b}}^2+\mathit{a}\mathit{b}\right)$
गणना​:
${\left(\mathit{a}+\mathit{b}\right)}^2$ = ${\mathit{a}}^2+{\mathit{b}}^2$ + 2ab
⇒ 72 = ${\mathit{a}}^2+{\mathit{b}}^2$ + 20
⇒ ${\mathit{a}}^2+{\mathit{b}}^2$ = 29
और, ${\mathit{a}}^3\mathit{–}{\mathit{b}}^3$ = (a – b) $\left({\mathit{a}}^2+{\mathit{b}}^2+\mathit{a}\mathit{b}\right)$
⇒ 117 = (a – b) (29 + 10)
⇒ (a – b) = 117/39
⇒ (a – b) = 3
स्मार्ट ट्रिक
दी गई शर्तों से, हम आसानी से ऐसा सोच सकते हैं 5 + 2 = 7 और 5 × 2 = 10.
इसलिये, a = 5 और b = 2.
∴ a – b = 5 – 2 = 3.