Question
Given $A = (x + 2, -2)$ and $B (11, 6)$. Find $x$ if $\text{AB} = 17.$
✓
Answer
$\text{AB} = 17$
$\text{AB}^2= 289$
$(11 - x - 2)^2+ (6 + 2)^2= 289$
$x^2+ 81 - 18x + 64 = 289$
$x^2- 18x - 144 = 0$
$x^2- 24x + 6x - 144 = 0$
$x(x - 24) + 6(x - 24) = 0$
$(x - 24) (x + 6) = 0$
$x = 24, -6$
$\text{AB}^2= 289$
$(11 - x - 2)^2+ (6 + 2)^2= 289$
$x^2+ 81 - 18x + 64 = 289$
$x^2- 18x - 144 = 0$
$x^2- 24x + 6x - 144 = 0$
$x(x - 24) + 6(x - 24) = 0$
$(x - 24) (x + 6) = 0$
$x = 24, -6$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
State whether the following number is rational or irrational$:\left(\frac{\sqrt{5}}{3 \sqrt{2}}\right)^2$
→In the given figure, ABCD is a rhombus in which $\angle A =72$. If $\angle CBD =x$, find the value of $x$.
→Simplify:
$\frac{3^n \times 9^{n+1}}{3^{n-1} \times 9^{n-1}}$
→$\frac{3^n \times 9^{n+1}}{3^{n-1} \times 9^{n-1}}$
Factorise:
$2 a^2+b c-2 a b-a c$
→$2 a^2+b c-2 a b-a c$
If one angle of a parallelogram is 90, show that each of its angles measures 90.
Find the distance between the following pairs of points$:(-a, -b)$ and $(a, b)$
→Find trinomial $($quadratic expression$),$ given below$,$ find whether it is factorisable or not. Factorise$,$ if possible.$3x^2+ 4x - 10$
→Using the standard formulae, expand:
(x- 2) (x - 3) (x + 4)
(x- 2) (x - 3) (x + 4)
find the value of $: \operatorname{cosec}^2 60^\circ- \tan^2 30^\circ$
→Convert each of the to exponential form:
$\log _3 81=4$
→$\log _3 81=4$