Question

The expressions 2(x² – 4x − 21) – (x − 7) (x +77) and (x − 7) (x + k) are equivalent. – What must be the value of k?​

Answers

  2. Answer:
    the value of k must be 2.
    Step-by-step explanation:
    To find the value of k, we can set the two expressions equal to each other and solve for k. We have:
    2(x² – 4x − 21) – (x − 7) (x +77) = (x − 7) (x + k)
    Expanding the left side gives:
    2x² – 8x – 42 – x² + 7x + 77 = x² – 7x + kx – 7k
    Combining like terms on both sides gives:
    x² – 15x + 119 – 7k = 0
    This is a quadratic equation in the form ax² + bx + c = 0. To solve for x, we can use the quadratic formula:
    x = (-b ± √(b² – 4ac)) / (2a)
    Substituting the values for a, b, and c, we get:
    x = (15 ± √(225 – 4(1)(119 – 7k))) / 2
    Since we are only interested in the value of k, we can disregard the solutions for x. Solving for k, we find that:
    k = (-119 + 225 – 4(1)(15)) / (2(-7))
    Simplifying this expression gives:
    k = (-119 + 225 + 60) / (-14)
    k = (-34) / (-14)
    k = 34/14
    k = 2
    Therefore, the value of k must be 2.

    Reply

Leave a Comment