Question

need steps .... plz help

Answer 1

$5) \\ {(k - 12)}{x}^{2} + 2(k - 12)x + 2 = 0 \\ {b}^{2} - 4ac = 0 \\ b =2( k - 12) \\ a =( k - 12) \\ c = 2 \\substitute \: a \:and \: b \: and \: c \: in \: above \: equation \\ {(2(k - 12))}^{2} - 4 (k - 12) \times 2 = 0 \\ 4 {(k - 12)}^{2} - 8(k - 12) = 0 \\ 4( {k}^{2} - 24k + 144) - 8k + 96 = 0 \\ 4 {k}^{2} - 96k + 576 - 8k + 96 = 0 \\ 4 {k}^{2} - 104k + 672 = 0 \\ {k}^{2} - 26k + 168 = 0 \\ {k}^{2} - 12k - 14k + 168 = 0 \\ k(k - 12) - 14(k - 12) = 0 \\ (k - 12)(k - 14) = 0 \\ k = 12 \: or \: 14$
k = 12 cannot be possible because x² and x coefficient will become 0

so, k = 14

6)51 = x + y
x*y = 378

378 = 2×3×3×3×7 = (2×3×7)×(3×3) = 42×9

so, x = 42
y = 9

x + y = 42 + 9 = 51

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