The expression n2 + n represents the total number of blocks used in the nth figure of a pattern. Use the equation n2 + n = 56 to determine which figure has 56 blocks.
2 answers:
This is an equation that is quadratic in form. so to solve th given equation we must first factor it: n2 + n = 56n2 + n - 56 = 0( n - 7 ) ( n + 8 ) = 0equate to zeron - 7 = 0n = 7andn + 8 = 0n = - 8 so the 7th figure has 56 blocks because there are no negative nth figure
We have to solve this quadratic equation for n to get <em>which figure has 56 blocks</em>.
For middle term factorization, we need <em>two numbers that multiplied gives us -56 and added gives us 1 (coefficient of n).</em>
<em>Such two numbers are </em><em>8</em> <em> and </em><em>-7</em> <em>. We can now write,</em>
<em> </em>
<u><em>"There is no negative figure number possible, so we disregard -8"</em></u>
Our answer is 7.
ANSWER: The 7th figure has 56 blocks.
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