Give the function: x^2 −7x−8=0 have two roots x_(1 ) and x_2 No solving the function Find: x_1 ^3 +x


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Question Number 192390 by TUN last updated on 16/May/23

$G i v e t h e f u n c t i o n :$ $x^{2} - 7 x - 8 = 0$ $h a v e t w o r o o t s x_{1} a n d x_{2}$ $N o s o l v i n g t h e f u n c t i o n$ $F i n d : x_{1}^{3} + x_{2} + 2023$
	Answered by deleteduser1 last updated on 17/May/23

	$x_{1}^{3} + x_{2} + 2023 = p; x_{2}^{3} + x_{1} + 2023 = q$ $p + q = {(x_{1} + x_{2})}^{3} - 3 x_{1} x_{2} (x_{1} + x_{2}) + x_{1} + x_{2} + 4046$ $x_{1} + x_{2} = 7; x_{1} x_{2} = - 8 \Rightarrow p + q = 343 + 168 + 7 + 4046 = 4564$ $p q = {(x_{1} x_{2})}^{3} + x_{1}^{4} + 2023 (x_{1}^{3} + x_{2}^{3}) + x_{2}^{4} + x_{1} x_{2} + 2023 (x_{2} + x_{1})$ $+ 2023^{2} = - 512 + [{(7^{2} + 16)}^{2} - 128] + 2023 (511) - 8 + 2023 (7)$ $+ 2023^{2} = 5144020$ $p + q = 4464; p q = 5144020 \Rightarrow p (4464 - p) = 5144020$ $\Rightarrow p = 2030, q = 2534 (u p t o s y m m e t r y)$
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