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(k - 1)(k + 1)(k - 2)(k + 2)

k=4

K/3 + k/4 = 1 LCD=12 *divide lcd by denominator* K(4) + K(3) = 12(1) 4k + 3k = 12 7k = 12 k=12/7

Equation: kx^2 +x^2 +kx +k +1 = 0 Using the discriminant: K^2 -4*(k +1)*(k +1) = 0 Expanding brackets: k^2 -4k^2 -8k -4 = 0 Collecting like terms: -3^2 -8k -4 = 0 Dividing all terms by -1: 3k^2 +8k +4 = 0 Factorizing the above: (3k +2)(k +2) = 0 meaning k = -2/3 or -2 Therefore possible values of k are either: -2/3 or -2

0

If: 6x^2 +2x +k = 0 has equal roots Then using the discriminant of b^2 -4ab=0: 4 -24k=0 => k=-4/-24 => k=1/6 Therefore the value of k = 1/6

If the equation has equal roots then the discriminant of b^2 -4ac = 0:- Equation: kx^2 +x^2 +kx +k +1 = 0 Discriminant: k^2 -4(k+1)(k+1) = 0 Multiplying out brackets: k^2 -4k^2 -8k -4 = 0 Collecting like terms: -3k^2 -8k -4 = 0 Divide all terms by -1: 3k^2 +8k +4 = 0 Factorizing: (3k +2)(k +2) = 0 => k = -2/3 or k = -2 Therefore possible values of k are -2/3 or -2

If: y = 3x +1 then y^2 = 9x^ +6x +1 If: x^2 +y^2 = k then 10^x^2 +6x +(1-k) = 0 Using the discriminant: -4 +40k = 0 Add 4 to both sides: 40k = 4 Divide both sides by 40: k = 1/10 Therefore the value of k is 1/10

Yes, they are exactly the same, both of them increment k in 1.

Yes, they are exactly the same, both of them increment k in 1.

Yes, they are exactly the same, both of them increment k in 1.

1 plus 1 plus 1 plus 1 equals 1 times 4. 1 times 4 equals 4. 4 minus 4 equals 0. 0

12 - 4 + k = 85 8 + k = 85 k = 77

It is 77

k+1

Equation: 2kx^2 -2x^2 +2kx +k -1 = 0 Using the discriminant: (2k)^2 -4*(2k -2)*(k -1) = 0 Solving for k in the discriminant: k = 2 + or - square root of 2

Equation: x^2 +2kx +10x +k^2 +5 = 0 Using the discriminant: (2k +10)^2 -4*1*(k^2 +5) = 0 Solving the discriminant: k = -2

50

2 k^2 - k - 4 = 0 2 (k^2 - (1/2)k - 2) = 0 2 ((k - 1/4)^2 - 1/16 - 2) = 0 2 ((k - 1/4)^2 - 33/16) = 0 2 (k - 1/4 - sqrt(33)/4)(k - 1/4 + sqrt(33)/4) = 0 32 (4k - 1 - sqrt(33))(4k - 1 + sqrt(33)) = 0

1 + 1 + 1 + 1/4 + 5/5 = 4 and 1/4

In K2MnF6, +1 for K, +4 for Mn and -1 for F In SbF5, +5 for Sb and -1 for F In KSbF6, +1 for K, +5 for Sb and -1 for F In MnF3, +3 for Mn and -1 for F In F2, 0 for F

Assuming the elements are integer type... a[k] ^= a[k+1]; a[k+1] ^= a[k]; a[k] ^= a[k+1]; ...but if they are not integer type... temp = a[k]; a[k] = a[k+1]; a[k+1] = temp;

k=8k+28 k-8k=28 -7k=28 k=-(28/4) k=-4

If: y = 3x +1 then y^2 = 9x^2 +6x +1 If: y^2 +x^2 = k then y^2 = k -x^2 So: 9x^2 +6x +1 = k -x^2 Transposing terms: 10x^2 +6x +(1 -k) = 0 Using the discriminant: 6^2 -4*10*(1 -k) = 0 Solving the discriminant: k = 1/10

1 + 4 + 4 = 9