‘Can be solved by most 13-year-olds in China’-3
Whole set
Given
Find the value of
.
Bonus: show that there is no need to solve the equation.
The answer is 9.
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1 solution
Rewrite the equation to get a 2 = 3 − a . . . ( 1 ) and − a − a 2 = − 3 . . . ( 2 ) . Substitute ( 1 ) to get a 2 ( a + 4 ) = ( 3 − a ) ( a + 4 ) = 1 2 − a − a 2 .
Then substitute ( 2 ) to get 1 2 − a − a 2 = 1 2 − 3 = 9 .
So the answer is 9 .