Question

12. Verify (-50)*(37+(-7)]=(-50)37+(-50)*(-7).
13. Find a pair of integers whose product is -21 and difference is -10.

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Answer 1

Step-by-step explanation:

1.

$( - 50) \times (37 + ( - 7)) = -( - 50)37 + ( - 50)( - 7) \\ - 50 \times 30 = - 1850 + 350 \\ - 1500 = - 1500 \\ lhs = rhs \\ hence ,\: \: proved$

2.

$given \\ xy = - 21 \\ x - y = - 10 \\ x = - 10 + y \\ substitut e\: \: this \: \: in \: \: 1st \: \: equation \\ ( - 10 + y)y = - 21 \\ {y}^{2} - 10y + 21 = 0 \\ {y}^{2} - 7y - 3y + 21 = 0 \\ y(y -7) - 3(y - 7) \\ (y - 7)(y - 3) \\ y = 7 \: \: or \: \: 3 \\ if \: \: y = 7 \: \: \\ x = \frac{ - 21}{7} = - 3$

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