SOLUTION: If a number is subtracted from 43,the principal square root of this difference is equal to the number decreased by 1, Find the number. A) {-6} B) {6,-7} c) {7} D) {-6,7}

Algebra ->  Finance -> SOLUTION: If a number is subtracted from 43,the principal square root of this difference is equal to the number decreased by 1, Find the number. A) {-6} B) {6,-7} c) {7} D) {-6,7}      Log On


   

Question 1123105: If a number is subtracted from 43,the principal square root of this difference is equal to the number decreased by 1, Find the number.
A) {-6}
B) {6,-7}
c) {7}
D) {-6,7}
Found 3 solutions by MathLover1, ikleyn, josmiceli:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2843+-+x%29+=+x+-+1+
%28sqrt%2843+-+x%29%29%5E2+=+%28x+-+1%29%5E2+
43+-+x+=+x%5E2+-2x%2B1+
0+=+x%5E2%2Bx+-2x%2B1-43+
+x%5E2+-x-42=0+
+x%5E2%2B6x+-7x-42=0+
+%28x%5E2%2B6x+%29-%287x%2B42%29=0+
+x%28x%2B6+%29-7%28x%2B6%29=0+
%28x+-+7%29+%28x+%2B+6%29+=+0

solutions:
if x+-+7+=+0 =>x=7
if +x+%2B+6+=+0 =>x=-6

check:
x=7
sqrt%2843+-+7%29+=+7-+1+=>sqrt%2836%29+=+6+=>6+=+6+ which is true
x=-6
sqrt%2843+-+%28-6%29%29+=-6-+1+=>sqrt%2849%29+=+-7+=>7+=+-7+ which is not true
so, your answer is C) {7}


Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.
sqrt%2843-x%29 = x - 1.


You may solve this equation, but you can also answer the question without solving equation.

Simply check the optional numbers by substituting the value of the number to both sides of the equation. 


The answer is option C).


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28+43+-+n+%29+=+n+-+1+
Square both sides
+43+-+n+=+%28+n+-+1+%29%5E2+
+43+-+n+=+n%5E2+-2n+%2B+1+
+n%5E2+-+n+-+42+=+0+
+%28+n+-+7+%29%2A%28+n+%2B+6+%29+=+0+
C) {7}
+-6+ does not work because you have
to take the negative square root