Question

I want the answer with explanation pls ​

Answer 1

Answer:

k = 6

Step-by-step explanation:

${x}^{2} - 8x + k = 0$

sum of squares of zeroes is equal to 40

this is 1st equation

${(x - a)}^{2} + {(x - b)}^{2} = 40$

$(x - a)(x - b) = {x}^{2} - 8x + k$

${x}^{2} - bx - ax + ab = {x}^{2} - 8x + k$

${x}^{2} - (b + a)x + ab = {x}^{2} - 8x + k$

comparing above equations

b + a = 8

k = ab

${(x - a)}^{2} + {(x - b)}^{2} = 40$

${x}^{2} + {a}^{2} - 2ax + {x}^{2} + {b}^{2} - 2bx = 40$

$2 {x}^{2} - 2(a + b)x + {a}^{2} + {b}^{2} = 40$

$2 {x}^{2} - 2(8)x + {a}^{2} + {b}^{2} = 40$

$2{x}^{2} - 16x + {a}^{2} + {b}^{2} = 40$

$2 {x}^{2} - 16x + {(a + b)}^{2} - 2ab = 40$

$2 {x}^{2} - 16x + 64 - 2k = 40$

$2 {x}^{2} - 16x + 24 - 2k = 0$

this is equation 2

from 1st equation

${x}^{2} - 8x = - k$

from 2nd equation

we can write in this way also

${x}^{2} - 8x + {x}^{2} - 8x + 24 - 2k = 0$

$- k - k + 24 - 2k = 0$

$- 4k + 24 = 0$

$4k = 24$

$k = 6$

Answer 2

Answer:

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