Question

If a - b = 9 and a² +b^2 = 881, where a and b are natural numbers. Find a + b



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Answer 1

Answer:

41

Step-by-step explanation:

$(a-b)^2=a^2-2ab+b^2$ --- 1

$(a-b)^2+2ab=a^2+b^2$ From 1

$81+2ab=881$

∴ $2ab=800$ --- 2

$(a+b)^2=a^2+2ab+b^2$

$(a+b)^2=(a-b)^2+4ab$ From 1

$(a+b)^2=81+1600$

$a+b=\sqrt{1681}$ From Definition Of Square Root

(As $a$ and $b$ are natural numbers, $a+b>0$)

∴ $a+b=41$

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Answer 2

Answer:

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