If x(2−√2)=y(2+√2)=1, find the value of x2−y2.
Answer:
2√2
- Since x(2−√2)=1, we can say that x=12−√2.
- Now if we multiply both numerator and denominator of the given fraction by 2+√2, we get:
12−√2×2+√22+√2
The denominator =(2−√2)(2+√2)=(22−(√2)2)=(4−2)=2 - From above steps we get x=2+√22.
- Similarly, for y(2+√2)=1, we can say that:
y=12+√2. - Now if we multiply both numerator and denominator by 2−√2, we get:
12+√2×2−√22−√2
The denominator =(2+√2)(2−√2)=(22−(√2)2)=(4−2)=2 - From the step 4 and 5, we get: y=2−√22.
- Now the value x2−y2=(2+√22)2−(2−√22)2=(22+2+4√24−22+2−4√24)=22+2+4√2−22−2+4√24=2√2