Question

29 Calculați: √(3-√√5)² + √(1-√√5)² ; c √(5-2√6)² +√√(3√6−7)² − √(√6 +4)² ; a ↳ √√(4−√7)² + √(√7 −2)² ; d √√(√8 −3)² + √(4−√18)² + √(11−√2)² . ​

Answer 1

Explicație pas cu pas:

3−√5 = √9−√5 > 0 => |3−√5| = 3−√5

1−√5 = √1−√5 < 0 => |1−√5| = √5−1

=> √(3−√5)² + √(1−√5)² = |3−√5| + |1−√5| = 3 − √5 + √5 − 1 = 2

.

5−2√6 = √25−√24 > 0 => |5−2√6| = 5−2√6

3√6−7 = √54−√49 > 0 => |3√6−7| = 3√6−7

√6+4 > 0 => |√6+4| = √6+4

=> √(5−2√6)² + √(3√6−7)² − √(√6+4)² = |5−2√6| + |3√6−7| − |√6+4| = 5 − 2√6 + 3√6 − 7 − (√6 + 4) = √6 − 2 − √6 − 4 = − 6

.

4−√7 = √16−√7 > 0 => |4−√7| = 4−√7

√7−2 = √7−√4> 0 => |√7 −2| = √7 −2

=> √(4−√7)² + √(√7−2)² = |4−√7| + |√7 −2| = 4 − √7 + √7 − 2 = 2

.

√8−3 = √8−√9 < 0 => |√8−3| = 3-√8

4−√18 = √16−√18 < 0 => |4−√18| = √18−4

11−√2 = √121−√2 > 0 => |11−√2| = 11−√2

=> √(√8−3)² + √(4−√18)² + √(11−√2)² = |√8−3| + |4−√18| + |11−√2| = |2√2−3| + |4−3√2| + |11−√2| = 3 − 2√2 + 3√2 − 4 + 11 − √2 = 3√2 − 3√2 + 14 − 4 = 10